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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 4, Pages 849–866
DOI: https://doi.org/10.33048/smzh.2020.61.409 (Mi smj6023) 		 
This article is cited in 2 scientific papers (total 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
Full-text PDF (560 kB) Citations (2)
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DOI: https://doi.org/10.33048/smzh.2020.61.409
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 |ξ|→∞ is a nonsmooth function of x.
Keywords: pseudodifferential operator, nonsmooth symbol, singular values, Weyl's asymptotics.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00472_а
The author was supported by the Russian Foundation for Basic Research (Grant 18–01–00472).
Received: 28.10.2019
Revised: 24.03.2020
Accepted: 08.04.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 4, Pages 671–686
DOI: https://doi.org/10.1134/S0037446620040096
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35R30
Language: Russian
Citation: A. I. Karol', “The singular values of compact pseudodifferential operators with spatially nonsmooth symbols”, Sibirsk. Mat. Zh., 61:4 (2020), 849–866; Siberian Math. J., 61:4 (2020), 671–686
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/smj6023
  • https://www.mathnet.ru/eng/smj/v61/i4/p849
    • This publication is cited in the following 2 articles:
    1. A. I. Karol, “Singulyarnye chisla kompaktnykh psevdodifferentsialnykh operatorov peremennogo poryadka s negladkim simvolom”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 50, Zap. nauchn. sem. POMI, 519, POMI, SPb., 2022, 67–104  mathnet
    2. A. I. Karol, A. I. Nazarov, “Spectral analysis for some multifractional Gaussian processes”, Russ. J. Math. Phys., 28:4 (2021), 488–500  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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