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Mat. Zametki, 2007, Volume 82, Issue 2, Pages 163–176 (Mi mz3799)  

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

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

DOI: https://doi.org/10.4213/mzm3799

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English version:
Mathematical Notes, 2007, 82:2, 141–152

Bibliographic databases:

UDC: 517.9
Received: 27.02.2006
Revised: 22.09.2006

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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    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. 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
    2. O. G. Avsyankin, “An algebra generated by multiplicative discrete convolution operators”, Russian Math. (Iz. VUZ), 55:1 (2011), 1–6  mathnet  crossref  mathscinet
    3. V. M. Deundyak, “Topological methods in solvability theory of multidimensional pair integral operators with homogeneous kernels of compact type”, Proc. Steklov Inst. Math., 278 (2012), 51–59  mathnet  crossref  mathscinet  isi
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