Moment Asymptotic Expansions of the Wavelet Transforms

TL;DR

This paper develops moment asymptotic expansions for the continuous wavelet transform using distribution theory, providing detailed analysis for large and small dilation parameters in various distributional spaces.

Contribution

It introduces a novel approach to asymptotic analysis of wavelet transforms through distribution theory, extending understanding of their behavior at different scales.

Findings

Derived asymptotic expansions for large dilation parameters.

Derived asymptotic expansions for small dilation parameters.

Extended the analysis to various distributional spaces.

Abstract

Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain wavelet transform.