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

Negrín, Emilio R.; Maan, Jeetendrasingh; Srivastava, Hari M.

doi:10.3390/math14091444

Open AccessArticle

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

by

Emilio R. Negrín

^1,2

,

Jeetendrasingh Maan

^3,*

and

Hari M. Srivastava

^4,5,6,7,8,9

¹

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

²

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

³

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

⁴

Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada

⁵

Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

⁶

Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

⁷

Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan

⁸

Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan

⁹

Section of Mathematics, International Telematic University Uninettuno, 39 Corso Vittorio Emanuele II, I-00186 Rome, Italy

^*

Author to whom correspondence should be addressed.

Mathematics 2026, 14(9), 1444; https://doi.org/10.3390/math14091444

Submission received: 16 March 2026 / Revised: 17 April 2026 / Accepted: 22 April 2026 / Published: 25 April 2026

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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.

Keywords: Hartley transforms; Parseval–Goldstein relations; Abelian theorems; distributions of compact support; generalized functions

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MDPI and ACS Style

Negrín, E.R.; Maan, J.; Srivastava, H.M. Parseval–Goldstein Identities and Abelian Theorems for the Hartley Transform over Distributions of Compact Support and Generalized Functions. Mathematics 2026, 14, 1444. https://doi.org/10.3390/math14091444

AMA Style

Negrín ER, Maan J, Srivastava HM. Parseval–Goldstein Identities and Abelian Theorems for the Hartley Transform over Distributions of Compact Support and Generalized Functions. Mathematics. 2026; 14(9):1444. https://doi.org/10.3390/math14091444

Chicago/Turabian Style

Negrín, Emilio R., Jeetendrasingh Maan, and Hari M. Srivastava. 2026. "Parseval–Goldstein Identities and Abelian Theorems for the Hartley Transform over Distributions of Compact Support and Generalized Functions" Mathematics 14, no. 9: 1444. https://doi.org/10.3390/math14091444

APA Style

Negrín, E. R., Maan, J., & Srivastava, H. M. (2026). Parseval–Goldstein Identities and Abelian Theorems for the Hartley Transform over Distributions of Compact Support and Generalized Functions. Mathematics, 14(9), 1444. https://doi.org/10.3390/math14091444

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

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