Year: 2024
Type: preprint
Abstract: We present a general framework of localized operators, i.e., operators whose matrix coefficients with respect to the Gabor frame are concentrated on the diagonal. We show that localized operators are bounded between modulation spaces, and we deduce their compactness from an easily verifiable weak compactness condition. We apply this abstract formalism to unify and extend existing theorems for pseudodifferential and Fourier integral operators, and to obtain new results for three-parameter pseudodifferential operators.
Source: arXiv (Cornell University)
Authors: Stockdale, Cody B., Waters, Cody
Institution: Clemson University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403781008