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Matematicheskie Zametki, 2016, Volume 99, Issue 3, Pages 323–332
DOI: https://doi.org/10.4213/mzm10708 (Mi mzm10708) 		 
This article is cited in 7 scientific papers (total in 7 papers)

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

O. G. Avsyankin

Southern Federal University, Rostov-on-Don
Full-text PDF (513 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm10708
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.
Received: 25.02.2015
Revised: 10.09.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 3, Pages 345–353
DOI: https://doi.org/10.1134/S0001434616030019
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
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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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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