Preprint Series 2009
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2009:01
S. Dekel,
Y. Han, and
P. Petrushev
We present a construction of anisotropic multiresolution and anisotropic wavelet frames based on multilevel ellipsoid covers (dilations) of R^n. The wavelets we construct are C^{infinity} functions, can have any prescribed number of vanishing moments and fast decay with respect to the anisotropic quasi-distance induced by the cover. The ...
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2009:02
K. Ivanov,
P. Petrushev, and
Y. Xu
Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate C^{infinity} cutoff functions. These tools are further employed to the development of the theory of weighted Triebel-Lizorkin and Besov spaces on [-1; 1]^d. It is also ...
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2009:03
S. Dekel and
P. Petrushev
In this survey we review the recently developed theory of anisotropic spaces and representations of functions based on anisotropic multilevel ellipsoid covers (dilations) of R^n. We also exhibit the relations of the ellipsoid cover approach to earlier concepts of anisotropic structures as well as to the framework of general ...
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2009:04
K. Ivanov and
P. Petrushev
A method for fast evaluation of spherical polynomials (band-limited functions) at many scattered points on the unit 2-d sphere is presented. The method relies on the sub-exponential localization of the father needlet kernels and their compatibility with spherical harmonics. It is fast, local, memory e±cient, numerically stable and with ...
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2009:05
Q. Du,
L. Ju, and
L. Tian
In this paper, we consider the phase separation on general surfaces by solving the nonlinear Cahn-Hilliard equation using a finite element method. A fully discrete approximation scheme is introduced, and we establish a priori estimates for the discrete solution that does not rely on any knowledge of the exact solution ...
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2009:06
P. Binev,
F. Blanco-Silva,
D. Blom,
W. Dahmen,
R. Sharpley, and
T. Vogt
We outline a new systematic approach to extracting high resolution information from HAADF-STEM images which will be beneficial to the characterization of beam sensitive materials. The idea is to treat several, possibly many low electron dose images with specially adapted digital image processing concepts at a minimum allowable spatial resolution ...
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2009:07
V. Temlyakov,
M. Yang, and
P. Ye
The main goal of this paper is to understand which properties of a basis are important for certain direct and inverse theorems in nonlinear approximation. We study greedy approximation with regard to bases with di®erent properties. We consider bases that are tensor products of univariate greedy bases. Some results ...
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