279 research outputs found
Asymptotic Uncorrelation for Mexican Needlets
We recall Mexican needlets from [5]. We derive an estimate for certain types
of Legendre series, which we apply to the statistical properties of Mexican
needlets. More precisely, we shall show that, under isotropy and Gaussianity
assumptions, the Mexican needlet coefficients of a random field on the sphere
are asymptotically uncorrelated, as the frequency parameter goes to infinity.
This property is important in the analysis of cosmic microwave background
radiation.Comment: 13 page
Homogeneous Besov spaces on stratified Lie groups and their wavelet characterization
We establish wavelet characterizations of homogeneous Besov spaces on
stratified Lie groups, both in terms of continuous and discrete wavelet
systems.
We first introduce a notion of homogeneous Besov space in
terms of a Littlewood-Paley-type decomposition, in analogy to the well-known
characterization of the Euclidean case. Such decompositions can be defined via
the spectral measure of a suitably chosen sub-Laplacian. We prove that the
scale of Besov spaces is independent of the precise choice of Littlewood-Paley
decomposition. In particular, different sub-Laplacians yield the same Besov
spaces.
We then turn to wavelet characterizations, first via continuous wavelet
transforms (which can be viewed as continuous-scale Littlewood-Paley
decompositions), then via discretely indexed systems. We prove the existence of
wavelet frames and associated atomic decomposition formulas for all homogeneous
Besov spaces , with and .Comment: 39 pages. This paper is to appear in Journal of Function Spaces and
Applications. arXiv admin note: substantial text overlap with arXiv:1008.451
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