S. Ivan Trapasso

@article{SST_25,

title = {On the existence of optimizers for nonlinear time-frequency concentration problems: the Wigner distribution },

author = {Federico Stra and Erling Svela and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2510.18683},

year  = {2026},

date = {2026-03-25},

urldate = {2025-10-21},

journal = {J. Math. Pures Appl. (to appear)},

abstract = {We prove that, for any measurable phase space subset (Omegasubsetmathbb{R}^{2d}) with (0<|Omega|<infty) and any (1le p < infty), the nonlinear concentration problem [sup_{f in L^2(mathbb{R}^d)setminus{0}}frac{|Wf|_{L^p(Omega)}}{|f|_{L^2}^2}] admits an optimizer, where (Wf) is the Wigner distribution of (f). The main obstruction is that (Wf) is covariant (not invariant) under time-frequency shifts, which impedes weak upper semicontinuity, so the effects of constructive interference must be taken into account. We close this compactness gap via concentration compactness for Heisenberg-type dislocations, together with a new asymptotic formula that quantifies the limiting contribution to concentration over (Omega) from asymptotically separated wave packets. When (p=infty) we also identify the sharp constant (2^d) and show that it is attained. We also discuss some related extensions: For (tau)-Wigner distributions with (tau in (0,1)) we isolate a chain phenomenon that obstructs the same strategy beyond the Wigner case ((tau=1/2)), while for the Born-Jordan distribution in (d=1) we obtain weak continuity, and thus existence of concentration optimizers for all (1le p<infty) (the (p=infty) supremum equals (pi) but is not attained).},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{CGPT_25,

title = {Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement},

author = {Elena Cordero and Gianluca Giacchi and Edoardo Pucci and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2508.02226

https://www.sciencedirect.com/science/article/pii/S0001870826000502/pdfft?md5=7ed5c060ac7fbd7b68081d585554055a&pid=1-s2.0-S0001870826000502-main.pdf, Open access PDF},

doi = {10.1016/j.aim.2026.110828},

year  = {2026},

date = {2026-02-02},

urldate = {2026-02-02},

journal = {Adv. Math.},

volume = {490},

pages = {110828},

abstract = {Motivated by the phase space analysis of Schrödinger evolution operators, in this paper we investigate how metaplectic operators are approximately diagonalized along the corresponding symplectic flows by exponentially localized Gabor wave packets. Quantitative bounds for the matrix coefficients arising in the Gabor wave packet decomposition of such operators are established, revealing precise exponential decay rates together with subtler dispersive and spreading phenomena. To this aim, we present several novel results concerning the time-frequency analysis of functions with controlled Gelfand-Shilov regularity, which are of independent interest. As a byproduct, we generalize Vemuri's Gaussian confinement results for the solutions of the quantum harmonic oscillator in two respects, namely by encompassing general exponential decay rates as well as arbitrary quadratic Schrödinger propagators. In particular, we extensively discuss some prominent models such as the harmonic oscillator, the free particle in a constant magnetic field and fractional Fourier transforms.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{T_JDE_25,

title = {Wave packet analysis of semigroups generated by quadratic differential operators},

author = {S. Ivan Trapasso},

url = {https://arxiv.org/abs/2408.11130

https://www.sciencedirect.com/science/article/pii/S0022039625007107/pdfft?md5=aacb48f12ad8e134791022b7e499449c&pid=1-s2.0-S0022039625007107-main.pdf, Open access PDF

},

doi = {10.1016/j.jde.2025.113683},

year  = {2025},

date = {2025-08-02},

urldate = {2025-08-02},

journal = {J. Differential Equations},

volume = {449},

issue = {2025},

pages = {113683},

abstract = {We perform a phase space analysis of evolution equations associated with the Weyl quantization (q^{mathrm{w}}) of a complex quadratic form (q) on (mathbb{R}^{2d}) with non-positive real part. In particular, we obtain pointwise bounds for the matrix coefficients of the Gabor wave packet decomposition of the generated semigroup (e^{tq^{mathrm{w}}}) if (mathrm{Re} (q) le 0) and the companion singular space associated is trivial. This result is then leveraged to achieve a comprehensive analysis of the phase regularity of (e^{tq^{mathrm{w}}}) with (mathrm{Re} (q) le 0), thereby extending the (L^2) analysis of quadratic semigroups initiated by Hitrik and Pravda-Starov to general modulation spaces (M^p(mathbb{R}^d)), (1 le p le infty), with optimal explicit bounds.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MNT_JFA_25,

title = {Phase space analysis of finite and infinite dimensional Fresnel integrals},

author = {Sonia Mazzucchi and Fabio Nicola and S. Ivan Trapasso },

url = {https://arxiv.org/abs/2403.20082

https://www.sciencedirect.com/science/article/pii/S0022123625001910/pdfft?md5=2323ac7b3fed88926bde9dafa29aba1c&pid=1-s2.0-S0022123625001910-main.pdf, Open access PDF},

doi = {10.1016/j.jfa.2025.111009},

year  = {2025},

date = {2025-04-15},

urldate = {2025-04-15},

journal = {J. Funct. Anal.},

volume = {289},

number = {111009},

issue = {8},

pages = {1--51},

abstract = {The full characterization of the class of Fresnel integrable functions is an open problem in functional analysis, with significant applications to mathematical physics (Feynman path integrals) and the analysis of the Schrödinger equation. In finite dimension, we prove the Fresnel integrability of functions in the Sjöstrand class (M^{infty,1}) - a family of continuous and bounded functions, locally enjoying the mild regularity of the Fourier transform of an integrable function. This result broadly extends the current knowledge on the Fresnel integrability of Fourier transforms of finite complex measures, and relies upon ideas and techniques of Gabor wave packet analysis. We also discuss the problem of designing infinite-dimensional extensions of this result, obtaining the first, non-trivial concrete realization of a general framework of projective functional extensions introduced by Albeverio and Mazzucchi. As an interesting byproduct, we obtain the exact (M^{infty,1} to L^infty) operator norm of the free Schrödinger evolution operator.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{NT_IMAIAI_25,

title = {Generalized moduli of continuity under irregular or random deformations via multiscale analysis},

author = {Fabio Nicola and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2104.11977

https://academic.oup.com/imaiai/article/doi/10.1093/imaiai/iaaf006/8108050?utm_source=authortollfreelink&utm_campaign=imaiai&utm_medium=email&guestAccessKey=87ddedf1-38c9-401d-b53d-cf41144903cf, Guest access PDF},

doi = {10.1093/imaiai/iaaf006},

year  = {2025},

date = {2025-04-08},

urldate = {2025-04-08},

journal = {Inf. Inference},

volume = {14},

number = {iaaf006},

issue = {2},

abstract = {Motivated by the problem of robustness to deformations of the input for deep convolutional neural networks, we identify signal classes which are inherently stable to irregular deformations induced by distortion fields (tauin L^infty(mathbb{R}^d;mathbb{R}^d)), to be characterized in terms of a generalized modulus of continuity associated with the deformation operator. Resorting to ideas of harmonic and multiscale analysis, we prove that for signals in multiresolution approximation spaces (U_s) at scale (s), stability in (L^2) holds in the regime (|tau|_{L^infty}/sll 1) - essentially as an effect of the uncertainty principle. Instability occurs when (|tau|_{L^infty}/sgg 1), and we provide a sharp upper bound for the asymptotic growth rate. The stability results are then extended to signals in the Besov space (B^{d/2}_{2,1}) tailored to the given multiresolution approximation. We also consider the case of more general time-frequency deformations. Finally, we provide stochastic versions of the aforementioned results, namely we study the issue of stability in mean when (tau(x)) is modeled as a random field (not bounded, in general) with identically distributed variables (|tau(x)|), (xinmathbb{R}^d).},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{AFST_JEMS_24,

title = {Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform},

author = {Giovanni S. Alberti and Alessandro Felisi and Matteo Santacesaria and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2302.03577},

doi = {10.4171/jems/1617},

year  = {2025},

date = {2025-04-01},

urldate = {2025-04-01},

journal = {J. Eur. Math. Soc. (JEMS)},

issue = {to appear},

abstract = {Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear measurements or subsampled isometries and has found many applications, including accelerated magnetic resonance imaging, which is modeled by the subsampled Fourier transform. In this work, we develop a general theory of infinite-dimensional compressed sensing for abstract inverse problems, possibly ill-posed, involving an arbitrary forward operator. This is achieved by considering a generalized restricted isometry property, and a quasi-diagonalization property of the forward map.



As a notable application, for the first time, we obtain rigorous recovery estimates for the sparse Radon transform (i.e., with a finite number of angles (theta_1,dots,theta_m)), which models computed tomography, in both the parallel-beam and the fan-beam settings. In the case when the unknown signal is (s)-sparse with respect to an orthonormal basis of compactly supported wavelets, we prove stable recovery under the condition [ mgtrsimß, ] up to logarithmic factors.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{T_TAMS_24,

title = {Phase space analysis of spectral multipliers for the twisted Laplacian},

author = {S. Ivan Trapasso},

url = {https://arxiv.org/abs/2306.00592},

doi = {10.1090/tran/9224},

year  = {2025},

date = {2025-02-01},

urldate = {2025-02-01},

journal = {Trans. Amer. Math. Soc.},

volume = {378},

number = {2},

pages = {967-999},

abstract = {We prove boundedness results on modulation and Wiener amalgam spaces for some families of spectral multipliers for the twisted Laplacian. We exploit the metaplectic equivalence relating the twisted Laplacian with a partial harmonic oscillator, leading to a general transference principle for the corresponding spectral multipliers. Our analysis encompasses powers of the twisted Laplacian and oscillating multipliers, with applications to the corresponding Schrödinger and wave flows. On the other hand, elaborating on the twisted convolution structure of the eigenprojections and its connection with the Weyl product of symbols, we obtain a complete picture of the boundedness of the heat flow for the twisted Laplacian. Results of the same kind are established for fractional heat flows via subordination.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{NT_JMPA_23,

title = {Stability of the scattering transform for deformations with minimal regularity},

author = {Fabio Nicola and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2205.11142

https://www.sciencedirect.com/science/article/pii/S0021782423001496/pdfft?md5=b95043909dc30fb3845bb0cac8a65b05&pid=1-s2.0-S0021782423001496-main.pdf, Open access PDF},

doi = {10.1016/j.matpur.2023.10.008},

year  = {2023},

date = {2023-12-31},

urldate = {2023-12-31},

journal = {J. Math. Pures Appl.},

volume = {180},

pages = {122–150},

publisher = {Elsevier Masson},

abstract = {Within the mathematical analysis of deep convolutional neural networks, the wavelet scattering transform introduced by Stéphane Mallat is a unique example of how the ideas of multiscale analysis can be combined with a cascade of modulus nonlinearities to build a nonexpansive, translation invariant signal representation with provable geometric stability properties, namely Lipschitz continuity to the action of small (C^2) diffeomorphisms - a remarkable result for both theoretical and practical purposes, inherently depending on the choice of the filters and their arrangement into a hierarchical architecture. In this note, we further investigate the intimate relationship between the scattering structure and the regularity of the deformation in the Hölder regularity scale (C^alpha), (alpha >0). We are able to precisely identify the stability threshold, proving that stability is still achievable for deformations of class (C^{alpha}), (alpha>1), whereas instability phenomena can occur at lower regularity levels modelled by (C^alpha), (0le alpha <1). While the behaviour at the threshold given by Lipschitz (or even (C^1)) regularity remains beyond reach, we are able to prove a stability bound in that case, up to (varepsilon) losses.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BMNTT_FCAA_23,

title = {On heat equations associated with fractional harmonic oscillators},

author = {Divyang G. Bhimani and Ramesh Manna and Fabio Nicola and Sundaram Thangavelu and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2210.07691

https://link.springer.com/content/pdf/10.1007/s13540-023-00208-6.pdf, Open access PDF},

doi = {10.1007/s13540-023-00208-6},

year  = {2023},

date = {2023-11-01},

urldate = {2023-11-01},

journal = {Fract. Calc. Appl. Anal.},

volume = {26},

number = {6},

pages = {2470–2492},

publisher = {Springer International Publishing Cham},

abstract = {We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator (e^{-tH^{beta}}), (t, beta>0), associated with the harmonic oscillator (H=-Delta + |x|^2). We then prove some local and global wellposedness results for nonlinear fractional heat equations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{NRT_CVPDE_23,

title = {On the existence of optimizers for time–frequency concentration problems},

author = {Fabio Nicola and José Luis Romero and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2112.09675

https://rdcu.be/cZmhU, View-only PDF},

doi = {10.1007/s00526-022-02358-6},

year  = {2023},

date = {2023-08-31},

urldate = {2023-08-31},

journal = {Calc. Var. Partial Differential Equations},

volume = {62},

number = {1},

pages = {1–21},

publisher = {Springer Berlin Heidelberg},

abstract = {We consider the problem of the maximum concentration in a fixed measurable subset (Omegasubsetmathbb{R}^{2d}) of the time-frequency space for functions (fin L^2(mathbb{R}^{d})). The notion of concentration can be made mathematically precise by considering the (L^p)-norm on (Omega) of some time-frequency distribution of (f) such as the ambiguity function (A(f)). We provide a positive answer to an open maximization problem, by showing that for every subset (Omegasubsetmathbb{R}^{2d}) of finite measure and every (1leq p<infty), there exists an optimizer for [



sup{|A(f)|_{L^p(Omega)}: fin L^2(mathbb{R}^{d}), |f|_{L^2}=1



}.



] The lack of weak upper semicontinuity and the invariance under time-frequency shifts make the problem challenging. The proof is based on concentration compactness with time-frequency shifts as dislocations, and certain integral bounds and asymptotic decoupling estimates for the ambiguity function. We also discuss the case (p=infty) and related optimization problems for the time correlation function, the cross-ambiguity function with a fixed window, and for functions in the modulation spaces (M^q(mathbb{R}^{d})), (0<q<2), equipped with continuous or discrete-type (quasi-)norms.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{T_IMRN_23,

title = {On the convergence of a novel time-slicing approximation scheme for Feynman path integrals},

author = {S. Ivan Trapasso},

url = {https://arxiv.org/abs/2107.00886

https://academic.oup.com/imrn/article-pdf/2023/14/11930/50903363/rnac179.pdf?guestAccessKey=da9e1686-c0c6-4dd2-ab3a-2c00bf8a8840, Guest access PDF},

doi = {10.1093/imrn/rnac179},

year  = {2023},

date = {2023-07-31},

urldate = {2023-07-31},

journal = {Int. Math. Res. Not. IMRN},

volume = {2023},

number = {14},

pages = {11930–11961},

publisher = {Oxford University Press},

abstract = {In this note we study the properties of a sequence of approximate propagators for the Schrödinger equation, in the spirit of Feynman's path integrals. Precisely, we consider Hamiltonian operators arising as the Weyl quantization of a quadratic form in phase space, plus a bounded potential perturbation in the form of a pseudodifferential operator with a rough symbol. It is known that the corresponding Schrödinger propagator is a generalized metaplectic operator. This naturally motivates the introduction of a manageable time slicing approximation consisting of operators of the same type. By means of techniques and function spaces of time-frequency analysis it is possible to obtain several convergence results with precise rates in terms of the mesh size of the time slicing subdivision. In particular, we prove convergence in the norm operator topology in (L^2), as well as pointwise convergence of the corresponding integral kernels for non-exceptional times.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{BMNTT_AIM_21,

title = {Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness},

author = {Divyang G. Bhimani and Ramesh Manna and Fabio Nicola and Sundaram Thangavelu and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2008.01226},

doi = {10.1016/j.aim.2021.107995},

year  = {2021},

date = {2021-12-03},

urldate = {2021-12-03},

journal = {Adv. Math.},

volume = {392},

pages = {107995},

publisher = {Academic Press},

abstract = {We study the Hermite operator (H=-Delta+|x|^2) in (mathbb{R}^d) and its fractional powers (H^beta), (beta>0) in phase space. Namely, we represent functions (f) via the so-called short-time Fourier, alias Fourier-Wigner or Bargmann transform (V_g f) ((g) being a fixed window function), and we measure their regularity and decay by means of mixed Lebesgue norms in phase space of (V_g f), that is in terms of membership to modulation spaces (M^{p,q}), (0< p,qleq infty). We prove the complete range of fixed-time estimates for the semigroup (e^{-tH^beta}) when acting on (M^{p,q}), for every (0< p,qleq infty), exhibiting the optimal global-in-time decay as well as phase-space smoothing. As an application, we establish global well-posedness for the nonlinear heat equation for (H^{beta}) with power-type nonlinearity (focusing or defocusing), with small initial data in modulation spaces or in Wiener amalgam spaces. We show that such a global solution exhibits the same optimal decay (e^{-c t}) as the solution of the corresponding linear equation, where (c=d^beta) is the bottom of the spectrum of (H^beta). This is in sharp contrast to what happens for the nonlinear focusing heat equation without potential, where blow-up in finite time always occurs for (even small) constant initial data - hence in (M^{infty,1}).},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{CNT_ACHA_21,

title = {Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators},

author = {Elena Cordero and Fabio Nicola and S. Ivan Trapasso},

url = {https://arxiv.org/abs/2005.03911},

doi = {10.1016/j.acha.2021.06.007},

year  = {2021},

date = {2021-11-30},

urldate = {2021-11-30},

journal = {Appl. Comput. Harmon. Anal.},

volume = {55},

pages = {405–425},

publisher = {Academic Press},

abstract = {Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent papers, including pseudodifferential, Fourier integral and metaplectic operators, with applications to time-frequency analysis of Schrödinger-type evolution equations. It has been proved that such operators are approximately diagonalized by Gabor wave packets. While the latter are expected to undergo some spreading phenomenon, there is no record of this issue in the aforementioned results. In this paper we prove refined estimates for the Gabor matrix of metaplectic operators, also of generalized type, where sparsity, spreading and dispersive properties are all noticeable. We provide applications to the propagation of singularities for the Schrödinger equation.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{NT_JFAA_20,

title = {A note on the HRT conjecture and a new uncertainty principle for the short-time Fourier transform},

author = {Fabio Nicola and S. Ivan Trapasso},

url = {https://arxiv.org/abs/1911.12241},

doi = {10.1007/s00041-020-09769-z},

year  = {2020},

date = {2020-07-30},

urldate = {2020-07-30},

journal = {J. Fourier Anal. Appl.},

volume = {26},

number = {4},

pages = {68},

publisher = {Springer US New York},

abstract = {In this note we provide a negative answer to a question raised by M. Kreisel concerning a condition on the short-time Fourier transform that would imply the HRT conjecture. In particular we provide a new type of uncertainty principle for the short-time Fourier transform which forbids the arrangement of an arbitrary "bump with fat tail" profile.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{T_JDE_20,

title = {Time-frequency analysis of the Dirac equation},

author = {S. Ivan Trapasso},

url = {https://arxiv.org/abs/1909.09842

https://www.sciencedirect.com/science/article/pii/S0022039620300577/pdfft?md5=9529d30135284078192dbd0cbc114288&pid=1-s2.0-S0022039620300577-main.pdf, Free access PDF},

doi = {10.1016/j.jde.2020.02.002},

year  = {2020},

date = {2020-07-15},

urldate = {2020-07-15},

journal = {J. Differential Equations},

volume = {269},

number = {3},

pages = {2477–2502},

publisher = {Academic Press},

abstract = {The purpose of this paper is to investigate several issues concerning the Dirac equation from a time-frequency analysis perspective. More precisely, we provide estimates in weighted modulation and Wiener amalgam spaces for the solutions of the Dirac equation with rough potentials. We focus in particular on bounded perturbations, arising as the Weyl quantization of suitable time-dependent symbols, as well as on quadratic and sub-quadratic non-smooth functions, hence generalizing the results in a recent paper by Kato and Naumkin. We then prove local well-posedness on the same function spaces for the nonlinear Dirac equation with a general nonlinearity, including power-type terms and the Thirring model. For this study we adopt the unifying framework of vector-valued time-frequency analysis as developed by Wahlberg; most of the preliminary results are stated under general assumptions and hence they may be of independent interest.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{NT_CMP_20,

title = {On the pointwise convergence of the integral kernels in the Feynman-Trotter formula},

author = {Fabio Nicola and S. Ivan Trapasso},

url = {https://arxiv.org/abs/1904.12531},

doi = {10.1007/s00220-019-03524-2},

year  = {2020},

date = {2020-06-01},

urldate = {2020-06-01},

journal = {Comm. Math. Phys.},

volume = {376},

number = {3},

pages = {2277–2299},

publisher = {Springer Berlin Heidelberg},

abstract = {We study path integrals in the Trotter-type form for the Schrödinger equation, where the Hamiltonian is the Weyl quantization of a real-valued quadratic form perturbed by a potential (V) in a class encompassing that - considered by Albeverio and Itô in celebrated papers - of Fourier transforms of complex measures. Essentially, (V) is bounded and has the regularity of a function whose Fourier transform is in (L^1). Whereas the strong convergence in (L^2) in the Trotter formula, as well as several related issues at the operator norm level are well understood, the original Feynman's idea concerned the subtler and widely open problem of the pointwise convergence of the corresponding probability amplitudes, that are the integral kernels of the approximation operators. We prove that, for the above class of potentials, such a convergence at the level of the integral kernels in fact occurs, uniformly on compact subsets and for every fixed time, except for certain exceptional time values for which the kernels are in general just distributions. Actually, theorems are stated for potentials in several function spaces arising in Harmonic Analysis, with corresponding convergence results. Proofs rely on Banach algebras techniques for pseudo-differential operators acting on such function spaces.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{CT_AA_20,

title = {Linear perturbations of the Wigner distribution and the Cohen class},

author = {Elena Cordero and S. Ivan Trapasso},

url = {https://arxiv.org/abs/1811.07795},

doi = {10.1142/S0219530519500052},

year  = {2020},

date = {2020-05-01},

urldate = {2020-05-01},

journal = {Anal. Appl.},

volume = {18},

number = {03},

pages = {385–422},

publisher = {World Scientific Publishing Company},

abstract = {The Wigner distribution is a milestone of Time-frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kind of modifications have been proposed. This contributions fits into this perspective. We introduce a family of phase-space representations of Wigner type associated with invertible matrices and explore their general properties. As main result, we provide a characterization for the Cohen's class. This feature suggests to interpret this family of representations as linear perturbations of the Wigner distribution. We show which of its properties survive under linear perturbations and which ones are truly distinctive of its central role.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{NT_JMP_19,

title = {Approximation of Feynman path integrals with non-smooth potentials},

author = {Fabio Nicola and S. Ivan Trapasso},

url = {https://arxiv.org/abs/1812.07487},

doi = {10.1063/1.5095852},

year  = {2019},

date = {2019-10-03},

urldate = {2019-10-03},

journal = {J. Math. Phys.},

volume = {60},

number = {10},

pages = {102103},

publisher = {AIP Publishing},

abstract = {We study the convergence in (L^2) of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the approximate propagators considered here arise from a series expansion of the action. The results are ultimately based on function spaces, tools and strategies which are typical of Harmonic and Time-frequency analysis.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{CNT_JFAA_19,

title = {Almost diagonalization of τ-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces},

author = {Elena Cordero and Fabio Nicola and S. Ivan Trapasso},

url = {https://arxiv.org/abs/1802.10314},

doi = {10.1007/s00041-018-09651-z},

year  = {2019},

date = {2019-08-15},

urldate = {2019-08-15},

journal = {J. Fourier Anal. Appl.},

volume = {25},

number = {4},

pages = {1927–1957},

publisher = {Springer US},

abstract = {In this paper we focus on the almost-diagonalization properties of (tau)-pseudodifferential operators using techniques from time-frequency analysis. Our function spaces are modulation spaces and the special class of Wiener amalgam spaces arising by considering the action of the Fourier transform of modulation spaces. A particular example is provided by the Sjöstrand class, for which Gröchenig exhibited the almost diagonalization of Weyl operators. We shall show that such result can be extended to any (tau)-pseudodifferential operator, for (tau in [0,1]), also with symbol in weighted Wiener amalgam spaces. As a consequence, we infer boundedness, algebra and Wiener properties for (tau)-pseudodifferential operators on Wiener amalgam and modulation spaces.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{CDT_JMAA_19,

title = {Norm estimates for τ-pseudodifferential operators in Wiener amalgam and modulation spaces},

author = {Elena Cordero and Lorenza D'Elia and S. Ivan Trapasso},

url = {https://arxiv.org/abs/1803.07865

https://www.sciencedirect.com/science/article/pii/S0022247X18309193/pdfft?md5=56e69bc9745c316f260d37420041913d&pid=1-s2.0-S0022247X18309193-main.pdf, Free access PDF},

doi = {https://doi.org/10.1016/j.jmaa.2018.10.090},

year  = {2019},

date = {2019-03-01},

urldate = {2019-03-01},

journal = {J. Math. Anal. Appl.},

volume = {471},

number = {1-2},

pages = {541–563},

publisher = {Academic Press},

abstract = {We study continuity properties on modulation spaces for (tau)-pseudodifferential operators with symbols (a) in Wiener amalgam spaces. We obtain boundedness results for (tau in (0,1)) whereas, in the end-points (tau=0) and (tau=1), the corresponding operators are in general unbounded. Furthermore, for (tau in (0,1)), we exhibit a function of (tau) which is an upper bound for the operator norm.



The continuity properties of (tau)-pseudodifferential operators, for any (tauin [0,1]), with symbols (a) in modulation spaces are well known. Here we find an upper bound for the operator norm which does not depend on the parameter (tau in [0,1]), as expected. Key ingredients are uniform continuity estimates for (tau)-Wigner distributions.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{DT_JPDO_18,

title = {Boundedness of pseudodifferential operators with symbols in Wiener amalgam spaces on modulation spaces},

author = {Lorenza D'Elia and S. Ivan Trapasso},

url = {https://arxiv.org/abs/1703.08989},

doi = {10.1007/s11868-017-0220-1},

year  = {2018},

date = {2018-12-01},

urldate = {2018-12-01},

journal = {J. Pseudo-Differ. Oper. Appl.},

volume = {9},

pages = {881–890},

publisher = {Springer International Publishing},

abstract = {This paper provides sufficient conditions for the boundedness of Weyl operators on modulation spaces. The Weyl symbols belong to Wiener amalgam spaces, or generalized modulation spaces, as recently renamed by their inventor Hans Feichtinger. This is the first result which relates symbols in Wiener amalgam spaces to operators acting on classical modulation spaces.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}