ANALYSIS OF CLIFFORD-WAVELET TRANSFORM IN $Cl_{(3,1)}$

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 19

Volume : 20 , Issue : 2
DOI: https://doi.org/10.56827/SEAJMMS.2024.2002.22
Author :
Shabnam Jahan Ansari (Mukesh Patel School of Technology Management & Engineering, SVKM s NMIMS, Mumbai, INDIA)
V. R. Lakshmi Gorty (Mukesh Patel School of Technology Management & Engineering, SVKM s NMIMS, Mumbai, INDIA)

Abstract

Clifford-wavelet transform in $L^2$-spaces is defined in space-time algebra $Cl_{(3,1)}$ of Minkowski space with orthonormal vector basis. The properties of Clifford-wavelet transform are established. Plancherel's theorem and reproducing kernel is demonstrated. The inversion formula for Clifford-wavelet transform is established. The study is supported with examples and applications from Mathematical Physics.

Keywords and Phrases

Clifford-wavelet transform, similitude group, multivector, inversion formula.

A.M.S. subject classification

15A66, 42B10, 42C40.

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