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Mat. Zametki, 2016, Volume 99, Issue 3, Pages 323–332 (Mi mz10708)  

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

$C^*$-Algebra of Integral Operators with Homogeneous Kernels and Oscillating Coefficients

O. G. Avsyankin

Southern Federal University, Rostov-on-Don

Abstract: We consider the $C^*$-algebra generated by multidimensional integral operators with $(-n)$th-order homogeneous kernels and by the operators of multiplication by oscillating coefficients of the form $|x|^{i\alpha}$. For this algebra, we construct an operator symbolic calculus and obtain necessary and sufficient conditions for the Fredholm property of an operator in terms of this calculus.

Keywords: integral operator, $C^*$-algebra, operator with oscillating coefficients, symbolic calculus, Fredholm property, index formula.

Funding Agency
This work was supported by the DFG–Russian Academy of Sciences foundation under grant 436 RUS 113/572.


DOI: https://doi.org/10.4213/mzm10708

Full text: PDF file (513 kB)
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English version:
Mathematical Notes, 2016, 99:3, 345–353

Bibliographic databases:

UDC: 517.9
Received: 25.02.2015
Revised: 10.09.2015

Citation: O. G. Avsyankin, “$C^*$-Algebra of Integral Operators with Homogeneous Kernels and Oscillating Coefficients”, Mat. Zametki, 99:3 (2016), 323–332; Math. Notes, 99:3 (2016), 345–353

Citation in format AMSBIB
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\by O.~G.~Avsyankin
\paper $C^*$-Algebra of Integral Operators with Homogeneous Kernels and Oscillating Coefficients
\jour Mat. Zametki
\yr 2016
\vol 99
\issue 3
\pages 323--332
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\vol 99
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\pages 345--353
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  • https://doi.org/10.4213/mzm10708
  • http://mi.mathnet.ru/eng/mz/v99/i3/p323

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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, “Invertibility of Multidimensional Integral Operators with Bihomogeneous Kernels”, Math. Notes, 108:2 (2020), 277–281  mathnet  crossref  crossref  mathscinet  isi  elib
    2. O. G. Avsyankin, “On integral operators with homogeneous kernels and trigonometric coefficients”, Russian Math. (Iz. VUZ), 65:4 (2021), 1–7  mathnet  crossref  crossref  isi
    3. O. G. Avsyankin, “On integral operators with homogeneous kernels in Morrey spaces”, Eurasian Math. J., 12:1 (2021), 92–96  mathnet  crossref
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