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Some results of Watson, Plancherel type integral transforms related to the Hartley, Fourier convolutions and applications
  • Tuan Trinh
Tuan Trinh
Electric Power University

Corresponding Author:[email protected]

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In this work, we study the Watson-type integral transforms for the convolutions related to the Hartley and Fourier transformations. We establish necessary and sufficient conditions for these operators to be unitary in the L 2 (R) space and get their inverse represented in the conjugate symmetric form. Furthermore, we also formulated the Plancherel-type theorem for the aforementioned operators and prove a sequence of functions that converge to the original function in the defined L 2 (R) norm. Next, we study the boundedness of the operators (T k ). Besides, showing the obtained results, we demonstrate how to use it to solve the class of integro-differential equations of Barbashin type, the differential equations, and the system of differential equations. And there are numerical examples given to illustrate these.
14 Sep 2021Submitted to Mathematical Methods in the Applied Sciences
15 Sep 2021Submission Checks Completed
15 Sep 2021Assigned to Editor
25 Sep 2021Reviewer(s) Assigned
20 Jan 2022Review(s) Completed, Editorial Evaluation Pending
09 Feb 2022Editorial Decision: Revise Major
14 Mar 20221st Revision Received
15 Mar 2022Submission Checks Completed
15 Mar 2022Assigned to Editor
19 Mar 2022Reviewer(s) Assigned
15 May 2022Review(s) Completed, Editorial Evaluation Pending
15 May 2022Editorial Decision: Accept