This article is cited in 9 papers

Convolution equations on a finite interval for a class of symbols having powerlike asymptotics at infinity

B. V. Pal'tsev


Abstract: A class of convolution equations is introduced on a finite interval, which is a generalization of a series of examples encountered in mathematical physics and other fields and for which a certain analogue of the Wiener–Hopf method is developed. As a corollary the Fredholm property is established for general convolution operators on a finite interval with symbols having polynomial growth at infinity in Sobolev spaces of generalized functions.
Bibliography: 31 titles.

UDC: 517.968.72 + 53

MSC: Primary 45E10; Secondary 47A53

Received: 10.10.1979

 English version: Mathematics of the USSR-Izvestiya, 1981, 16:2, 291–356

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