Finite Interval Convolution Operators with Transmission Property |
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Authors: | L P Castro R Duduchava F-O Speck |
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Institution: | (1) Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal;(2) A. Razmadze Mathematical Institute, Academy of Sciences of Georgia, 1, M. Alexidze str., Tbilisi, 93, Georgia;(3) Department of Mathematics, U.T.L., Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal |
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Abstract: | We study convolution operators in Bessel potential spaces and (fractional) Sobolev spaces over a finite interval. The main purpose of the investigation is to find conditions on the convolution kernel or on a Fourier symbol of these operators under which the solutions inherit higher regularity from the data. We provide conditions which ensure the transmission property for the finite interval convolution operators between Bessel potential spaces and Sobolev spaces. These conditions lead to smoothness preserving properties of operators defined in the above-mentioned spaces where the kernel, cokernel and, therefore, indices do not depend on the order of differentiability. In the case of invertibility of the finite interval convolution operator, a representation of its inverse is presented in terms of the canonical factorization of a related Fourier symbol matrix function. |
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Keywords: | Primary 47B35 Secondary 47A05 46E35 45E10 |
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