Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 127–130 (Mi into181)  
This article is cited in 4 scientific papers (total in 4 papers)

Fundamental operator-valued functions of singular integrodifferential operators in Banach spaces

M. V. Falaleev

Irkutsk State University
Full-text PDF (256 kB) Citations (4)
Abstract: In this paper, using methods of the theory of generalized functions in Banach spaces, we examine the Cauchy problem for an abstract integrodifferential equation of a specific type. Under the assumption that there exist the complete Jordan structure of the differential part of the equation and the order of the zero of the kernel of the integral part, the fundamental operator-valued function (the fundamental solution) is constructed for the corresponding integrodifferential operator, which is used for further investigations of the problem.
Keywords: Banach space, Fredholm operator, generalized function, fundamental solution.
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 782–785
DOI: https://doi.org/10.1007/s10958-018-3789-x
Bibliographic databases:
Document Type: Article
UDC: 517.983.5, 517.968.7
MSC: 34G10, 45K05, 45N05
Language: Russian
Citation: M. V. Falaleev, “Fundamental operator-valued functions of singular integrodifferential operators in Banach spaces”, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132, VINITI, Moscow, 2017, 127–130; J. Math. Sci. (N. Y.), 230:5 (2018), 782–785
Citation in format AMSBIB
\Bibitem{Fal17}
\by M.~V.~Falaleev
\paper Fundamental operator-valued functions of singular integrodifferential operators in Banach spaces
\inbook Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 132
\pages 127--130
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into181}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801401}
\zmath{https://zbmath.org/?q=an:1394.45015}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 782--785
\crossref{https://doi.org/10.1007/s10958-018-3789-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044442315}
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  • https://www.mathnet.ru/eng/into/v132/p127
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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