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Mathematics of the USSR-Sbornik, 1977, Volume 33, Issue 1, Pages 43–61
DOI: https://doi.org/10.1070/SM1977v033n01ABEH002413
(Mi sm2936)
 

This article is cited in 24 scientific papers (total in 24 papers)

On a class of one-dimensional singular pseudodifferential operators

I. A. Kipriyanov, V. V. Katrakhov
References:
Abstract: The paper is devoted to studying the method of the Sonin and Poisson transmutation operators for ordinary differential operators with variable coefficients. A new class of singular pseudodifferential operators is introduced which is closed under multiplication and which contains differential operators with singular coefficients, in particular, the Bessel operator. It is shown that after application of transmutation operators the original operator with variable coefficients (even a differential operator) is transformed into a classical pseudodifferential operator. The converse is also true: a pseuddifferential operator is transformed into a singular pseudodifferential operator. In all cases formulas are given for computing the symbols.
Bibliography: 6 titles.
Received: 14.12.1976
Bibliographic databases:
UDC: 517.9
MSC: Primary 35S05; Secondary 47E05, 35Q05
Language: English
Original paper language: Russian
Citation: I. A. Kipriyanov, V. V. Katrakhov, “On a class of one-dimensional singular pseudodifferential operators”, Math. USSR-Sb., 33:1 (1977), 43–61
Citation in format AMSBIB
\Bibitem{KipKat77}
\by I.~A.~Kipriyanov, V.~V.~Katrakhov
\paper On~a~class of one-dimensional singular pseudodifferential operators
\jour Math. USSR-Sb.
\yr 1977
\vol 33
\issue 1
\pages 43--61
\mathnet{http://mi.mathnet.ru//eng/sm2936}
\crossref{https://doi.org/10.1070/SM1977v033n01ABEH002413}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=513018}
\zmath{https://zbmath.org/?q=an:0365.47028|0401.47025}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1977GQ33000004}
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  • https://doi.org/10.1070/SM1977v033n01ABEH002413
  • https://www.mathnet.ru/eng/sm/v146/i1/p49
  • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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