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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Acknowledgment
The author is grateful to A. I. Nazarov for useful discussions.
Funding
The author was supported by the Russian Foundation for Basic Research (Grant 18–01–00472).
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Karol, A.I. The Singular Values of Compact Pseudodifferential Operators with Spatially Nonsmooth Symbols. Sib Math J 61, 671–686 (2020). https://doi.org/10.1134/S0037446620040096
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DOI: https://doi.org/10.1134/S0037446620040096