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 Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 3, Pages 714–726 (Mi izv2035)

On a class of integral equations of convolution type and its applications

N. K. Karapetyants, S. G. Samko

Abstract: Operators of convolution type with variable coefficients are investigated in spaces of series $E$ commonly employed for such operators and supplemented by the spaces $M_0^{\sup}$, $M_0^{\mathrm{mes}}$, $M^{\sup}$, $M^{\mathrm{mes}}$ of bounded measurable functions. The properties of these new spaces are investigated. Conditions insuring that operators are of the Noether type are investigated and the index of operators with coefficients from these spaces are calculated. A theorem asserting the coincidence of zeros in these spaces is stated. The results are applied to investigate conditions for integral equations with homogeneous kernels to be of Noether type. For the last class the structure of zeros is clarified in the case of constant coefficients.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:3, 731–744

Bibliographic databases:

UDC: 517.9
MSC: 45E10

Citation: N. K. Karapetyants, S. G. Samko, “On a class of integral equations of convolution type and its applications”, Izv. Akad. Nauk SSSR Ser. Mat., 35:3 (1971), 714–726; Math. USSR-Izv., 5:3 (1971), 731–744

Citation in format AMSBIB
\Bibitem{KarSam71} \by N.~K.~Karapetyants, S.~G.~Samko \paper On a~class of integral equations of convolution type and its applications \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1971 \vol 35 \issue 3 \pages 714--726 \mathnet{http://mi.mathnet.ru/izv2035} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=285937} \zmath{https://zbmath.org/?q=an:0213.38801} \transl \jour Math. USSR-Izv. \yr 1971 \vol 5 \issue 3 \pages 731--744 \crossref{https://doi.org/10.1070/IM1971v005n03ABEH001106}