Decomposition of spaces of distributions induced by tensor product bases

Details Decomposition of spaces of distributions induced by tensor product bases Decomposition of spaces of distributions induced by tensor product bases

2009-02-16

arxiv.org/abs/0902.2601v1

Mathematics

Classical Analysis and ODEs

42 pages

Scientific paper

Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate $C^\infty$ 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 shown how kernels induced by cross product bases can be constructed and utilized for the development of weighted spaces of distributions on products of multidimensional ball, cube, sphere or other domains.

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