The Mexican hat wavelet Stieltjes transform

Abstract

In this paper, we define the Mexican hat wavelet Stieltjes transform (MHWST) by applying the concept of Mexican hat wavelet transform \cite{rspathak}. We study some basic properties of Mexican hat wavelet Stieltjes transform to obtain its inversion formula. A unified approach is applied to obtain necessary and sufficient conditions for the same. Moreover, simplified construction for the jump operator is also presented for the Mexican hat wavelet Stieltjes transform.