34 citations · 50 across the 22 of their papers we have counts for
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math.CA2007
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 $…
math.ST2007★ 34 cited
Needlet algorithms for estimation in inverse problems
Gérard Kerkyacharian, Pencho Petrushev, Dominique Picard +1
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis.…
math.CA2007★ 1 cited
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…