Decomposition of spaces of distributions induced by tensor product bases

2009/02/16 by Kamen G. Ivanov, Kamen Ivanov, Pencho Petrushev +4
Engineering · Mathematics · #Advanced Harmonic Analysis Research #Advanced Numerical Analysis Techniques #Mathematical Analysis and Transform Methods #math.CA #msc:42B35 #msc:42C10 #msc:42C40

paper · pdf · doi:10.48550/arxiv.0902.2601

42 pages

arxiv created 2009/02/16 · arxiv updated 2009/12/01

Abstract

Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate C^∞ 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.

Related

• Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
• Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces
• Decomposition of spaces of distributions induced by Hermite expansions
• Tensor products for Gelfand-Shilov and Pilipović distribution spaces
• Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation