S. Ivan Trapasso

@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, arXiv 

https://www.sciencedirect.com/science/article/pii/S0001870826000502/pdfft?md5=7ed5c060ac7fbd7b68081d585554055a&pid=1-s2.0-S0001870826000502-main.pdf, 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 = {Gabor analysis, mathematical physics, metaplectic operators, Schrödinger equations, time-frequency analysis},

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, arXiv 

https://academic.oup.com/imrn/article-pdf/2023/14/11930/50903363/rnac179.pdf?guestAccessKey=da9e1686-c0c6-4dd2-ab3a-2c00bf8a8840, 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 = {Feynman path integrals, mathematical physics, pseudodifferential operators, Schrödinger equations, time-frequency analysis},

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, arXiv},

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 = {Gabor analysis, mathematical physics, metaplectic operators, Schrödinger equations, time-frequency analysis},

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, arXiv},

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 = {Feynman path integrals, mathematical physics, pseudodifferential operators, Schrödinger equations, time-frequency analysis},

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, arXiv},

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 = {Feynman path integrals, mathematical physics, Schrödinger equations, time-frequency analysis},

pubstate = {published},

tppubtype = {article}

}