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Parseval–Goldstein Identities and Abelian Theorems for the Hartley Transform over Distributions of Compact Support and Generalized Functions

Author

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  • Emilio R. Negrín

    (Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de La Laguna (ULL), Campus de Anchieta, ES-38271 La Laguna, Tenerife, Spain
    Instituto de Matemáticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), ULL Campus de Anchieta, ES-38271 La Laguna, Tenerife, Spain)

  • Jeetendrasingh Maan

    (Department of Mathematics and Scientific Computing, National Institute of Technology, Hamirpur 177005, India)

  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
    Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan)

Abstract

This work develops an analytical framework for the Hartley transform, which, unlike the Fourier transform, converts real-valued functions into real-valued functions. We derive Parseval–Goldstein-type identities for suitable classes of functions and establish Abelian theorems in the setting of compactly supported distributions and generalized functions. Moreover, a finite formulation of the Hartley transform is constructed and analyzed within the spaces of distributions of compact support and generalized functions.

Suggested Citation

  • Emilio R. Negrín & Jeetendrasingh Maan & Hari M. Srivastava, 2026. "Parseval–Goldstein Identities and Abelian Theorems for the Hartley Transform over Distributions of Compact Support and Generalized Functions," Mathematics, MDPI, vol. 14(9), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:9:p:1444-:d:1928380
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