1 citations · 2 across the 6 of their papers we have counts for
5 papers · 1 filter
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 interval with Jacobi weights
Pencho Petrushev, Yuan Xu
As is well known the kernel of the orthogonal projector onto the polynomials of degree in $L^2(w_{\a,\b}, [-1, 1])$ with $w_{\a,\b}(t) = (1-t)^\a(1+t)^\b$ can be written in ter…