Spectral Properties for Pseudodifferential Operators via Weighted Modulation Spaces

A. Askari-Hemmat, Z. Rahbani

Abstract


In this paper we deal with this question: considering spectral representation of a positive trace-class integral operator, if its orthonormal eigenvectors are in modulation space $M^p_m$? This question actually provide a new framework for studying the connection between operator theory and modulation spaces. Here we use some Schatten class properties of seudodifferential operators to give a positive answer to this question. Also we investigate convergence conditions for eigenvectors of such operators.

Keywords


Frames; Gabor systems; Modulation spaces; Wilson bases; Spectral representation; trace-class operators

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v3i3.210

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