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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 4, Pages 739–764 (Mi izv1729)  

This article is cited in 2 scientific papers (total in 2 papers)

On the spectrum of a class of differential operators and some imbedding theorems

O. D. Apyshev, M. Otelbaev


Abstract: The spectral properties of the operator
$$ Lu=\frac{(-1)^{n+k}}{\rho(t)}(\frac{u(t)}{\rho(t)})^{(2n+2k)}+\frac{(-1)^k}{\rho(t)}(V^2(t)(\frac{u(t)}{\rho(t)})^{(k)})^{(k)}\qquad(n,k\geqslant1) $$
are considered. A criterion for the nuclearity of the resolvent, two-sided estimates of the nuclear norm, Green's functions on the diagonal and the norms of the inverse operator are obtained.
Bibliography: 21 titles.

Full text: PDF file (1739 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1980, 15:1, 1–24

Bibliographic databases:

UDC: 513.88+517.514
MSC: Primary 34B25, 47E05; Secondary 47A40, 46E35
Received: 19.09.1978

Citation: O. D. Apyshev, M. Otelbaev, “On the spectrum of a class of differential operators and some imbedding theorems”, Izv. Akad. Nauk SSSR Ser. Mat., 43:4 (1979), 739–764; Math. USSR-Izv., 15:1 (1980), 1–24

Citation in format AMSBIB
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\by O.~D.~Apyshev, M.~Otelbaev
\paper On the spectrum of a~class of differential operators and some imbedding theorems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 4
\pages 739--764
\mathnet{http://mi.mathnet.ru/izv1729}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=548503}
\zmath{https://zbmath.org/?q=an:0446.47039|0418.47022}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 1
\pages 1--24
\crossref{https://doi.org/10.1070/IM1980v015n01ABEH001190}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980LB83500001}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. D. Stepanov, “Two-weighted estimates of Riemann–Liouville integrals”, Math. USSR-Izv., 36:3 (1991), 669–681  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. E. N. Lomakina, “Estimates for the approximation numbers of one class of integral operators. I”, Siberian Math. J., 44:1 (2003), 147–159  mathnet  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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