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Fundamental inequalities for the iterated Fourier-cosine convolution with Gaussian weight and its application

arXiv.org, 2024-04

2024. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;http://creativecommons.org/licenses/by-nc-nd/4.0 ;EISSN: 2331-8422 ;DOI: 10.48550/arxiv.2404.03609

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  • Title:
    Fundamental inequalities for the iterated Fourier-cosine convolution with Gaussian weight and its application
  • Author: Nguyen Thi Hong Phuong ; Trinh Tuan ; Lai, Tien Minh
  • Subjects: Convolution ; Integral equations ; Mathematics - Classical Analysis and ODEs ; Mathematics - Functional Analysis ; Trigonometric functions
  • Is Part Of: arXiv.org, 2024-04
  • Description: Derived from the results in (Math. Nachr., 283(12):1758-1770, 2010), in this paper, we devoted to studying the boundedness properties for Fourier-cosine convolution weighted by Gaussian functions via Young's type theorem and Saitoh's type inequality. New norm estimations in the weighted space are obtained and application of the corresponding class of convolutions in Fredholm's second kind of integral equation is discussed. The conditions for the solvability of this equation in \(L_1\) space are also found, along with the analysis of an illustrative example, which exemplifies that the present object and method solve cases that are not under the conditions of previously known techniques.
  • Publisher: Ithaca: Cornell University Library, arXiv.org
  • Language: English
  • Identifier: EISSN: 2331-8422
    DOI: 10.48550/arxiv.2404.03609
  • Source: Directory of Open Access Scholarly Resources (ROAD)
    arXiv.org
    AUTh Library subscriptions: ProQuest Central
    Open Access: Freely Accessible Journals by multiple vendors
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