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Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1199–1216 (Mi smj1248)  

This article is cited in 5 scientific papers (total in 5 papers)

On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree $-n$

O. G. Avsyankin, N. K. Karapetyants

Rostov State University

Abstract: We study the limit behavior of the spectral characteristics of truncated multidimensional integral operators whose kernels are homogeneous of degree $-n$ and invariant under the rotation group $SO(n)$. We prove that the limit of the $\varepsilon$-pseudospectra of the truncated operators $K_{\tau}$ as $\tau\to0$ is equal to the union of the $\varepsilon$-pseudospectra of the original operator $K$ and the “transposed” operator $\widetilde{K}$.

Keywords: multidimensional integral operator, homogeneous kernel, spectrum, pseudospectrum, truncated operator

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English version:
Siberian Mathematical Journal, 2003, 44:6, 935–950

Bibliographic databases:

UDC: 517.9
Received: 04.06.2003

Citation: O. G. Avsyankin, N. K. Karapetyants, “On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree $-n$”, Sibirsk. Mat. Zh., 44:6 (2003), 1199–1216; Siberian Math. J., 44:6 (2003), 935–950

Citation in format AMSBIB
\Bibitem{AvsKar03}
\by O.~G.~Avsyankin, N.~K.~Karapetyants
\paper On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree~$-n$
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 6
\pages 1199--1216
\mathnet{http://mi.mathnet.ru/smj1248}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2034928}
\zmath{https://zbmath.org/?q=an:1036.45001}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 935--950
\crossref{https://doi.org/10.1023/B:SIMJ.0000007469.86630.6b}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000187464000001}


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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. O. G. Avsyankin, “Multidimensional integral operators with bihomogeneous kernels: A projection method and pseudospectra”, Siberian Math. J., 47:3 (2006), 410–421  mathnet  crossref  mathscinet  zmath  isi
    2. O. G. Avsyankin, “On the Noethericity of multidimensional integral operators with homogeneous and quasi-homogeneous kernels”, Russian Math. (Iz. VUZ), 50:11 (2006), 1–8  mathnet  mathscinet
    3. 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
    4. O. G. Avsyankin, “On the $C^*$-algebra generated by multiplicative discrete convolution operators with oscillating coefficients”, Siberian Math. J., 55:6 (2014), 977–983  mathnet  crossref  mathscinet  isi
    5. O. G. Avsyankin, A. M. Kovalchuk, “Parnye integralnye operatory s odnorodnymi yadrami, vozmuschennye operatorami multiplikativnogo sdviga”, Vladikavk. matem. zhurn., 20:1 (2018), 10–20  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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