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 Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 7, Pages 3–17 (Mi ivm8715)

The boundedness and the Fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients

V. M. Deundyak, E. I. Miroshnikova

Chair of Algebra and Discrete Mathematics, Southern Federal University, Rostov-on-Don, Russia

Abstract: In the space $L_p(\mathbb R^n)$, $1<p<\infty$, we study a new wide class of integral operators with anisotropically homogeneous kernels. We obtain sufficient conditions for the boundedness of operators from this class. We consider the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type and multiplicatively slowly oscillating coefficients. We establish a relationship between this algebra and multidimensional convolution operators, and construct a symbolic calculus for it. We also obtain necessary and sufficient conditions for the Fredholm property of operators from this algebra.

Keywords: integral operators, homogeneous kernels, convolution operators, boundedness, fredholmness.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:7, 1–14

Bibliographic databases:

Document Type: Article
UDC: 517.9

Citation: V. M. Deundyak, E. I. Miroshnikova, “The boundedness and the Fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 7, 3–17; Russian Math. (Iz. VUZ), 56:7 (2012), 1–14

Citation in format AMSBIB
\Bibitem{DeuMir12} \by V.~M.~Deundyak, E.~I.~Miroshnikova \paper The boundedness and the Fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2012 \issue 7 \pages 3--17 \mathnet{http://mi.mathnet.ru/ivm8715} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3077457} \transl \jour Russian Math. (Iz. VUZ) \yr 2012 \vol 56 \issue 7 \pages 1--14 \crossref{https://doi.org/10.3103/S1066369X12070018} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866271321} 

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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. Elena M., “Boundedness and Invertibility of Multidimensional Integral Operators With Anisotropically Homogeneous Kernels in Weighted l-P-Spaces”, 10Th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences (Icnpaa 2014), AIP Conference Proceedings, 1637, ed. Sivasundaram S., Amer Inst Physics, 2014, 663–672
2. A. V. Lukin, “Primenenie lokalnogo podkhoda Simonenko–Kozaka v teorii proektsionnykh metodov resheniya uravnenii svertki s operatornymi koeffitsientami”, Vladikavk. matem. zhurn., 18:2 (2016), 55–66
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