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Bibliographic Details
Main Authors: Stockdale, Cody B., Waters, Cody
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2409.15096
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author Stockdale, Cody B.
Waters, Cody
author_facet Stockdale, Cody B.
Waters, Cody
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2409_15096
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Compact pseudodifferential and Fourier integral operators via localization
Stockdale, Cody B.
Waters, Cody
Classical Analysis and ODEs
Analysis of PDEs
Functional Analysis
47G30
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.
title Compact pseudodifferential and Fourier integral operators via localization
topic Classical Analysis and ODEs
Analysis of PDEs
Functional Analysis
47G30
url https://arxiv.org/abs/2409.15096