Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds
arXiv:1002.3841
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.
References in corpus (7)
- Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets
- The non-Gaussian Cold Spot in the 3-year WMAP data
- Exact reconstruction with directional wavelets on the sphere
- Search for non-Gaussianity in pixel, harmonic and wavelet space: compared and combined
- Cosmological non-Gaussian Signature Detection: Comparing Performance of Different Statistical Tests
- Complex data processing: fast wavelet analysis on the sphere
- Nearly tight frames of spin wavelets on the sphere
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- Heat kernel generated frames in the setting of Dirichlet spaces
- Adaptive Nonparametric Regression on Spin Fiber Bundles