2020•Siberian Mathematical JournalRequires access

The Singular Values of Compact Pseudodifferential Operators with Spatially Nonsmooth Symbols

A. I. Karol’

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 \( x \) .

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Key concepts: Mathematics, Pseudodifferential operators, Smoothness, Order (exchange), Pure mathematics, Function (biology), Compact space, Mathematical analysis