Journal of Geometric Analysis

, Volume 21, Issue 2, pp 334–371 | Cite as

Band-Limited Localized Parseval Frames and Besov Spaces on Compact Homogeneous Manifolds

Article

Abstract

In the last decade, methods based on various kinds of spherical wavelet bases have found applications in virtually all areas where analysis of spherical data is required, including cosmology, weather prediction, and geodesy. In particular, the so-called needlets (= band-limited Parseval frames) have become an important tool for the analysis of Cosmic Microwave Background (CMB) temperature data. The goal of the present paper is to construct band-limited and highly localized Parseval frames on general compact homogeneous manifolds. Our construction can be considered as an analogue of the well-known φ-transform on Euclidean spaces.

Keywords

Compact homogeneous manifold Wavelets Laplace operator Eigenfunctions 

Mathematics Subject Classification (2000)

43A85 42C40 41A17 41A10 

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Copyright information

© Mathematica Josephina, Inc. 2010

Authors and Affiliations

  1. 1.Department of MathematicsStony Brook UniversityStony BrookUSA
  2. 2.Department of MathematicsTemple UniversityPhiladelphiaUSA

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