FOURIER TYPE TRANSFORMS AND THEIR CONVOLUTIONS ON $\mathbb{R}^n$

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 172

Volume : 18 , Issue : 2
DOI: 10.56827/SEAJMMS.2022.1802.10
Author :
A. M. Mahajan (Department of Mathematics, Walchand College of Arts and Science, Solapur - 413006, Maharasthra, INDIA)
M. S. Chaudhary (Department of Mathematics, Shivaji University, Kolhapur - 416004, Maharashtra, INDIA)

Abstract

In this paper the operational properties of two integral transforms of Fourier type are defined. The purpose of the study is to define the convolution of the Fourier type transform on $L_1(\mathbb{R}^n)$ and $L_2(\mathbb{R}^n)$. Also we obtained the Inversion, Uniqueness and Plancherel's theorem of these two transform. Lastely we have applied these transform to differential equation of higher order for the solution.

Keywords and Phrases

Plancherel's theorem, Convolution, Hermite function.

A.M.S. subject classification

42A38, 44A35.

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