A Family of Mexican Hat Wavelet Stieltjes Transform for Unbounded Non-decreasing Functions
摘要
In the present article, we examine the characteristics of the Mexican hat wavelet Stieltjes transform (MHWST) for a specific set of functions belonging to one of the sub-class of bounded variation functions. The subset comprises functions that are unbounded and non-decreasing. Further, a unified approach is applied to establish a uniqueness theorem and subsequently derive a representation theorem for the MHWST.