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Matematicheskie Zametki, 2007, Volume 82, Issue 2, Pages 163–176
DOI: https://doi.org/10.4213/mzm3799 (Mi mzm3799) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients

O. G. Avsyankin, V. M. Deundyak

Rostov State University
Full-text PDF (559 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm3799
Abstract: In this paper, we study the Banach algebra $\mathfrak B$ generated by multidimensional integral operators whose kernels are homogeneous functions of degree $(-n)$ invariant with respect to the rotation group $SO(n)$ and by the operators of multiplication by radial weakly oscillating functions. A symbolic calculus is developed for the algebra $\mathfrak B$. The Fredholm property and the formula for calculating the index are described in terms of this calculus.
Keywords: Fredholm property, integral operators, operator algebra, index of a Fredholm operator, Banach algebra, locally oscillating function.
Received: 27.02.2006
Revised: 22.09.2006
English version:
Mathematical Notes, 2007, Volume 82, Issue 2, Pages 141–152
DOI: https://doi.org/10.1134/S0001434607070188
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: O. G. Avsyankin, V. M. Deundyak, “On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients”, Mat. Zametki, 82:2 (2007), 163–176; Math. Notes, 82:2 (2007), 141–152
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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