Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds

2010/02/19 by Daryl Geller, Geller, Daryl, Isaac Z. Pesenson +1 · 2 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #41A10 #41A17 #42C40 #43A85 #Advanced Differential Geometry Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques #Spectral Theory (math.SP) #math.CA #math.FA #math.SP #msc:41A10 #msc:41A17 #msc:42C40 #msc:43A85

paper · pdf · doi:10.48550/arxiv.1002.3841

arxiv created 2010/02/19 · openalex publication_date 2010/02/19 · arxiv updated 2010/02/26 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

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 phi-transform on Euclidean spaces.

Citations

• Nearly tight frames of spin wavelets on the sphere

Cited by

• Scattering Networks on Noncommutative Finite Groups
• Cubature formulas and discrete fourier transform on compact manifolds

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