This article is cited in 2 papers

The singular values of compact pseudodifferential operators with spatially nonsmooth symbols

A. I. Karol'

St. Petersburg State University, Mathematics and Mechanics Faculty

Abstract: Considering compact pseudodifferential operators with symbols whose smoothness in $x$ vanishes on a prescribed set, we obtain some validity conditions for the Weyl spectral asymptotics of singular values. These results are applied to the symbols whose decay order as $|\xi| \to \infty$ is a nonsmooth function of $x$.

Keywords: pseudodifferential operator, nonsmooth symbol, singular values, Weyl's asymptotics.

UDC: 517.9

MSC: 35R30

Received: 28.10.2019
Revised: 24.03.2020
Accepted: 08.04.2020

DOI: 10.33048/smzh.2020.61.409

 English version: Siberian Mathematical Journal, 2020, 61:4, 671–686

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