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8 papers · 1 filter
Decomposition of spaces of distributions induced by tensor product bases
Kamen Ivanov, Pencho Petrushev, Yuan Xu
Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate cutoff fu…
Sub-exponentially localized kernels and frames induced by orthogonal expansions
Kamen Ivanov, Pencho Petrushev, Yuan Xu
The aim of this paper is to construct sup-exponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, sp…
Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions
G. Kerkyacharian, P. Petrushev, D. Picard +1
A pair of dual frames with almost exponentially localized elements (needlets) are constructed on $\RR_+^d$ based on Laguerre functions. It is shown that the Triebel-Lizorkin and Be…
Decomposition of spaces of distributions induced by Hermite expansions
Pencho Petrushev, Yuan Xu
Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $…
Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
G. Kyriazis, P. Petrushev, Yuan Xu
Weighted Triebel-Lizorkin and Besov spaces on the unit ball in $\Rd$ with weights $\W(x)= (1-|x|^2)^{μ-1/2}$, , are introduced and explored. A decomposition scheme is…
Localized polynomial frames on the ball
Pencho Petrushev, Yuan Xu
Almost exponentially localized polynomial kernels are constructed on the unit ball in $\RR^d$ with weights %functions , , by smoothing out…