RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (559 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.9
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
\Bibitem{AvsDeu07} \by O.~G.~Avsyankin, V.~M.~Deundyak \paper On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients \jour Mat. Zametki \yr 2007 \vol 82 \issue 2 \pages 163--176 \mathnet{http://mi.mathnet.ru/mz3799} \crossref{https://doi.org/10.4213/mzm3799} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2374894} \elib{http://elibrary.ru/item.asp?id=12844011} \transl \jour Math. Notes \yr 2007 \vol 82 \issue 2 \pages 141--152 \crossref{https://doi.org/10.1134/S0001434607070188} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000249410700018} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-58649099623} 

• http://mi.mathnet.ru/eng/mz3799
• https://doi.org/10.4213/mzm3799
• http://mi.mathnet.ru/eng/mz/v82/i2/p163

 SHARE:

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
2. O. G. Avsyankin, “An algebra generated by multiplicative discrete convolution operators”, Russian Math. (Iz. VUZ), 55:1 (2011), 1–6
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
•  Number of views: This page: 421 Full text: 139 References: 43 First page: 8