A continuous spherical wavelet transform for~$\mathcal C(\mathcal S^n)$

TL;DR

This paper introduces a new wavelet transform on the n-dimensional sphere that uses polynomial wavelets at each scale and guarantees convergence of the inverse transform for continuous functions in the supremum norm.

Contribution

It constructs a spherical wavelet family with polynomial wavelets at each scale and proves convergence of the inverse transform in the supremum norm.

Findings

Wavelet family constructed on the n-sphere with polynomial wavelets.

Inverse transform converges in the supremum norm for continuous functions.

Provides a new tool for analysis on spherical domains.

Abstract

In the present paper, a wavelet family over the $n$-dimensional sphere is constructed such that for each scale the wavelet is a polynomial and the inverse wavelet transform of a continuous function converges in the supremum norm.