Time-frequency analysis of Born–Jordan pseudodifferential operators

Preprint revised TIME FREQUENCY ANALYSIS OF PSEUDODIFFERENTIAL OPERATORS

In this paper we apply a time frequency approach to the study of pseudodi er ential operators Both the Weyl and the Kohn Nirenberg correspondences are considered In order to quantify the time frequency content of a function or distribution we use certain function spaces called modulation spaces We deduce a time frequency characterization of the twisted product of two symbols and and we show tha...

Pseudodifferential Operators

The study of pseudodifferential operators emerged in the 1960’s, having its origins in the study of singular integro-differential operators. In fact, Friedrichs and Lax coined the term “pseudodifferential operator” in their 1965 paper entitled “Boundary Value Problems for First Order Operators”. Since that time, pseudodifferential operators have proved useful in many arenas of modern analysis a...

Time - Frequency Analysis of Localization Operators

Integral Operators, Pseudodifferential Operators, and Gabor Frames

This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Dau...

Localization Operators via Time-Frequency Analysis

A systematic overview of localization operators using a time-frequency approach is given. Sufficient and necessary regularity results for localization operators with symbols and windows living in various function spaces (such as L or modulation spaces) are discussed. Finally, an exact and an asymptotic product formulae are presented.