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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 271, Pages 56–62 (Mi znsl1347)  
On solution of the functional equations of the 1st and 2nd kind whose the transformations with orthogonal coordinats

G. Ya. Areshkin

Military Technical University
Full-text PDF (147 kB)
Abstract: In this paper we introduce the notion of coordinats for a linear continuous transformation of Hilbert space $H$. We develop the complete solvability theory for the functional equations of the 1st and 2nd kind with kernels having orthogonal coordinats and we obtain all such solutions. In particular, this theory is applicable to equations with compact operator.
Received: 08.11.2000
English version:
Journal of Mathematical Sciences (New York), 2003, Volume 115, Issue 6, Pages 2731–2734
DOI: https://doi.org/10.1023/A:1023309500657
Bibliographic databases:
UDC: 517.98
Language: Russian
Citation: G. Ya. Areshkin, “On solution of the functional equations of the 1st and 2nd kind whose the transformations with orthogonal coordinats”, Boundary-value problems of mathematical physics and related problems of function theory. Part 31, Zap. Nauchn. Sem. POMI, 271, POMI, St. Petersburg, 2000, 56–62; J. Math. Sci. (N. Y.), 115:6 (2003), 2731–2734
Citation in format AMSBIB
\Bibitem{Are00}
\by G.~Ya.~Areshkin
\paper On solution of the functional equations of the 1st and 2nd kind whose the transformations with orthogonal coordinats
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~31
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 271
\pages 56--62
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1347}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1810608}
\zmath{https://zbmath.org/?q=an:1025.47007}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 115
\issue 6
\pages 2731--2734
\crossref{https://doi.org/10.1023/A:1023309500657}
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