Searcharxiv⌕ Search

arXiv subjects

Salvatore Ivan Trapasso

Publications and source records attributed to Salvatore Ivan Trapasso.

4 recordsLinked to original sources
arXiv2025

Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement

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.

math.AP↗
arXiv2018

Almost diagonalization of $τ$-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces

In this paper we focus on the almost-diagonalization properties of $τ$-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 $τ$-pseudodifferential operator, for $τ\in [0,1]$, also with symbol in weighted Wiener amalgam spaces. As a consequence, we infer boundedness, algebra and Wiener properties for $τ$-pseudodifferential operators on Wiener amalgam and modulation spaces.

math.FA↗
arXiv2018

Norm Estimates for $τ$-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces

We study continuity properties on modulation spaces for $τ$-pseudodifferential operators with symbols $a$ in Wiener amalgam spaces. We obtain boundedness results for $τ\in (0,1)$ whereas, in the end-points $τ=0$ and $τ=1$, the corresponding operators are in general unbounded. Furthermore, for $τ\in (0,1)$, we exhibit a function of $τ$ which is an upper bound for the operator norm. The continuity properties of $τ$-pseudodifferential operators, for any $τ\in [0,1]$, 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 $τ\in [0,1]$, as expected. Key ingredients are uniform continuity estimates for $τ$-Wigner distributions.

math.FA↗