Continuous wavelet transforms on $n$-dimensional spheres

TL;DR

This paper develops a comprehensive theory of continuous wavelet transforms on n-dimensional spheres, including isometry, Euclidean limit, and relationships to other wavelet methods, expanding the mathematical framework for spherical signal analysis.

Contribution

It introduces a new theory of linear wavelets on n-dimensional spheres and proves key properties for nonzonal bilinear wavelets, advancing spherical wavelet analysis.

Findings

Proved isometry and Euclidean limit for nonzonal bilinear wavelets

Developed a theory of linear wavelets on n-spheres

Discussed relationships to other wavelet constructions

Abstract

In this paper, we are concerned with $n$-dimensional spherical wavelets derived from the theory of approximate identities. For nonzonal bilinear wavelets introduced by Ebert \emph{et al.} in 2009 we prove isometry and Euclidean limit property. Further, we develop a theory of linear wavelets. In the end, we discuss the relationship to other wavelet constructions.