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Sibirsk. Mat. Zh., 2006, Volume 47, Number 3, Pages 501–513 (Mi smj872)  

This article is cited in 3 scientific papers (total in 3 papers)

Multidimensional integral operators with bihomogeneous kernels: A projection method and pseudospectra

O. G. Avsyankin

Rostov State University

Abstract: We consider multidimensional integral operators with bihomogeneous and rotation invariant kernels. For such operators we obtain a criterion for applicability of a projection method in the scalar and matrix cases and describe the limit behavior of the $\varepsilon$-pseudospectra of the truncated operators $A_{\tau_1,\tau_2}$ as $\tau_1\to0$, $\tau_2\to0$.

Keywords: integral operator, truncated operator, projection method, spectrum, pseudospectrum, $C^*$-algebra

Full text: PDF file (237 kB)
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English version:
Siberian Mathematical Journal, 2006, 47:3, 410–421

Bibliographic databases:

UDC: 517.9
Received: 17.03.2005

Citation: O. G. Avsyankin, “Multidimensional integral operators with bihomogeneous kernels: A projection method and pseudospectra”, Sibirsk. Mat. Zh., 47:3 (2006), 501–513; Siberian Math. J., 47:3 (2006), 410–421

Citation in format AMSBIB
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\by O.~G.~Avsyankin
\paper Multidimensional integral operators with bihomogeneous kernels: A projection method and pseudospectra
\jour Sibirsk. Mat. Zh.
\yr 2006
\vol 47
\issue 3
\pages 501--513
\mathnet{http://mi.mathnet.ru/smj872}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2249162}
\zmath{https://zbmath.org/?q=an:1115.47058}
\transl
\jour Siberian Math. J.
\yr 2006
\vol 47
\issue 3
\pages 410--421
\crossref{https://doi.org/10.1007/s11202-006-0053-2}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33744765182}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. G. Avsyankin, “The spectra and singular values of multidimensional integral operators with bihomogeneous kernels”, Siberian Math. J., 49:3 (2008), 389–394  mathnet  crossref  mathscinet  zmath  isi
    2. V. M. Deundyak, “Multidimensional Integral Operators with Homogeneous Kernels of Compact Type and Multiplicatively Weakly Oscillating Coefficients”, Math. Notes, 87:5 (2010), 672–686  mathnet  crossref  crossref  mathscinet  isi
    3. V. M. Deundyak, A. V. Lukin, “Proektsionnyi metod resheniya uravnenii dlya mnogomernykh operatorov s anizotropno odnorodnymi yadrami kompaktnogo tipa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:2 (2019), 153–165  mathnet  crossref  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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