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<p>We will present qualitative properties and applications of convolutions associated with the Hartley and Fourier transforms, when weighted by Gaussian functions, in a multidimensional framework. This will include the consideration of those convolutions in appropriate Lebesgue spaces (also with weights), boundedness results for the corresponding operators, Young- and Hausdorff–Young-type inequalities, a Plancherel-type theorem, and a Watson-type theory. In terms of possible applications, they will be illustrated by analyzing the solvability of classes of Fredholm-type integral equations, Barbashin-type integro-differential equations, and a class of Cauchy-type problems. Illustrative examples are provided to demonstrate the validity and applicability of the results.</p>

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Qualitative properties and applications of convolutions associated with Hartley and Fourier transforms

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • L. P. Castro,
  • N. T. H. Phuong,
  • T. Tuan

摘要

We will present qualitative properties and applications of convolutions associated with the Hartley and Fourier transforms, when weighted by Gaussian functions, in a multidimensional framework. This will include the consideration of those convolutions in appropriate Lebesgue spaces (also with weights), boundedness results for the corresponding operators, Young- and Hausdorff–Young-type inequalities, a Plancherel-type theorem, and a Watson-type theory. In terms of possible applications, they will be illustrated by analyzing the solvability of classes of Fredholm-type integral equations, Barbashin-type integro-differential equations, and a class of Cauchy-type problems. Illustrative examples are provided to demonstrate the validity and applicability of the results.