Characteristics of Mexican hat wavelet transform in a class of generalized quotient space

Abstract

In this paper, Mexican hat wavelet transformation is defined on the space of tempered generalized quotients by employing the structure of exchange property. We study the exchange property for the Mexican hat wavelet transform by applying the theory of the Mexican hat wavelet transform of distributions. Further, different properties of Mexican hat wavelet transform are investigated on the space of tempered generalized quotients.