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

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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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Correspondence to Daryl Geller.

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I.Z. Pesenson was supported in part by the National Geospatial-Intelligence Agency University Research Initiative (NURI), grant HM1582-08-1-0019.

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Geller, D., Pesenson, I.Z. Band-Limited Localized Parseval Frames and Besov Spaces on Compact Homogeneous Manifolds. J Geom Anal 21, 334–371 (2011). https://doi.org/10.1007/s12220-010-9150-3

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