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, arXiv 

https://www.sciencedirect.com/science/article/pii/S0021782426000656/pdfft?md5=6dd623c3313b1a76deecf9a455f9f414&pid=1-s2.0-S0021782426000656-main.pdf, PDF},

doi = {10.1016/j.matpur.2026.103919},

year  = {2026},

date = {2026-03-25},

urldate = {2026-03-25},

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

volume = {201},

pages = {103919},

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 = {concentration problems, quantum harmonic analysis, time-frequency analysis, time-frequency distributions, Wigner distributions},

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, arXiv},

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 = {harmonic analysis, time-frequency analysis, time-frequency distributions, Wigner distributions},

pubstate = {published},

tppubtype = {article}

}