New polyconvolution product for Fourier‐cosine and Laplace integral operators and their applications
Trinh Tuan
Abstract:The goal of this paper is to introduce the notion of polyconvolution for Fourier‐cosine, Laplace integral operators, and its applications. The structure of this polyconvolution operator and associated integral transforms are investigated in detail. The Watson‐type theorem is given, to establish necessary and sufficient conditions for this operator to be isometric isomorphism (unitary) on
, and to get its inverse represented in the conjugate symmetric form. The correlation between the existence of polyconvolut… Show more
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