Abstract
This note deals with a class of convolution operators of the first kind on a finite interval. Necessary and sufficient conditions for such an operator to be Fredholm are given. The argument is based on a process of reduction of convolution-type operators on a finite interval to operators of the same type on the half line.
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References
Bastos, M. A. and dos Santos, A. F.: Convolution equations of the first kind on a finite interval in Sobolev spaces,Integral Equations and Operator Theory, to appear.
Hungerford, T. W.: Algebra, Springer Verlag, New York, etc., 1974.
Karlovich, Yu. I. and Spitkovskiî, I. M.: On the Noetherian property of certain singular integral operators with matrix coefficients of class SAP and systems of convolution equations on a finite interval connected with them.Dokl. Akad. Nauk SSSR 269 (1983), 531–535,(Russian) = Soviet Math. Dokl. 27 (1983), 358–363.
Karlovich, Yu. I. and Spitkovskiî, I. M.: On the theory of systems of convolution type equations with semi-almost-periodic symbols in spaces of Bessel potentials,Dokl. Akad. Nauk SSSR 286 (1986), 799–803,(Russian) = Soviet Math. Dokl. 33 (1986), 180–184.
Pal'cev, B. V.: A generalization of the Wiener-Hopf method for convolution equations on a finite interval with symbols having power-like asymptotics at infinity,Math. Sb. 113 (155) (1980), 355–399,(Russian) = Math. USSR Sb. 41 (1982), 289–328.
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Research supported by the Netherlands organization for scientific research (NWO).
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Kuijper, A.B. A note on first kind convolution equations on a finite interval. Integr equ oper theory 14, 146–152 (1991). https://doi.org/10.1007/BF01194931
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DOI: https://doi.org/10.1007/BF01194931