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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 7, Pages 3–17 (Mi ivm8715)  
This article is cited in 5 scientific papers (total in 5 papers)

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
Full-text PDF (304 kB) Citations (5)
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Abstract: In the space Lp(Rn), 1<p<∞, 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.
Received: 14.07.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 7, Pages 1–14
DOI: https://doi.org/10.3103/S1066369X12070018
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
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
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  • https://www.mathnet.ru/eng/ivm8715
  • https://www.mathnet.ru/eng/ivm/y2012/i7/p3
    • This publication is cited in the following 5 articles:
    1. V. V. Denisenko, V. M. Deundyak, “Fredholm Property of Integral Operators with Homogeneous Kernels of Compact Type in the L2 Space on the Heisenberg Group”, Proc. Steklov Inst. Math., 308 (2020), 155–167  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. M. Deundyak, A. V. Lukin, “Proektsionnyi metod resheniya uravnenii dlya mnogomernykh operatorov s anizotropno odnorodnymi yadrami kompaktnogo tipa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:2 (2019), 153–165  mathnet  crossref  elib
    3. V. V. Denisenko, V. M. Deundyak, “Obratimost integralnykh operatorov s odnorodnymi yadrami kompaktnogo tipa na gruppe Geizenberga”, Matematicheskaya fizika i kompyuternoe modelirovanie, 21:3 (2018), 5–18  mathnet  crossref
    4. 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  mathnet
    5. 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  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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