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New results on the invertibility of the finite interval convolution operator

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Abstract

Conditions for the invertibility and explicit formulas for the inverse of the convolution operator on a finite interval are obtained making use of solutions of corona problems. Using these results, a family of classes of functions is defined for which the study of invertibility can be carried through. An example of one class of this family is presented and a smaller class, for which the calculations are simpler, is more thoroughly studied.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1096, LISBOA CODEX, PORTUGAL

    P. A. Lopes & A. F. dos Santos

Authors
  1. P. A. Lopes
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  2. A. F. dos Santos
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Work sponsored by F.C.T. (Portugal) under Project Praxis XXi/2/2.1/MAT/441/94

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Lopes, P.A., dos Santos, A.F. New results on the invertibility of the finite interval convolution operator. Integr equ oper theory 38, 317–333 (2000). https://doi.org/10.1007/BF01291717

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  • DOI: https://doi.org/10.1007/BF01291717

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