Wavelets on the 3–dimensional Ball

Abstract

In this article wavelets on a ball in ℝ 3 are introduced. Corresponding properties like an approximate identity and decomposition/reconstruction (scale step property) are proved. The advantage of this approach compared to a classical Fourier analysis in orthogonal polynomials is a better localization of the used ansatz functions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)