Band-Limited Localized Parseval Frames and Besov Spaces on Compact Homogeneous Manifolds |
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Authors: | Daryl Geller Isaac Z Pesenson |
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Institution: | 1.Department of Mathematics,Stony Brook University,Stony Brook,USA;2.Department of Mathematics,Temple University,Philadelphia,USA |
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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. |
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