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New polyconvolution product for Fourier-cosine and Laplace integral operators and their applications
  • Trinh Tuan
Trinh Tuan
Electric Power University

Corresponding Author:tuantrinhpsac@yahoo.com

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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 is investigated in detail. The Watson-type theorem is given, to establish necessary and sufficient conditions for this operator to be unitary on L 2 ( R ) , and to get its inverse represented in the conjugate symmetric form. The correlation between the existence of polyconvolution with some weighted spaces is shown, and Young’s type theorem, as well as the norm-inequalities in weighted space, are also obtained. As applications of the Fourier cosine–Laplace polyconvolution, the solvability in closed-form of some classes for integral equations of Toeplitz plus Hankel type and integro-differential equations of Barbashin type is also considered. Several examples are provided for illustrating the obtained results to ensure their validity and applicability.
07 Feb 2023Submitted to Mathematical Methods in the Applied Sciences
07 Feb 2023Assigned to Editor
07 Feb 2023Submission Checks Completed
14 Feb 2023Review(s) Completed, Editorial Evaluation Pending
16 Feb 2023Reviewer(s) Assigned