Continuous wavelet transforms on $n$-dimensional spheres

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.

32 pages

References in corpus (3)

• Continuous Wavelets on Compact Manifolds
• Diffusive wavelets on groups and homogeneous spaces
• Poisson wavelets on $n$-dimensional spheres

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• Wavelet methods in partial differential equations on spheres