FOURIER TYPE TRANSFORMS AND THEIR CONVOLUTIONS ON R n

A. M. Mahajan; M. S. Chaudhary

doi:10.56827/SEAJMMS.2022.1802.10

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

DOI: https://doi.org/10.56827/SEAJMMS.2022.1802.10

Keywords: Plancherel’s theorem, Convolution, Hermite function.

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 L1(R n ) and L2(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.