Browsing by Author "Petrushev, P."
Now showing items 1-15 of 15
-
Article
Anisotropic Franklin bases on polygonal domains
Kyriazis, George C.; Park, K.; Petrushev, P. (2006)Franklin systems induced by Courant elements over multilevel nested triangulations of polygonal domains in ℝ2 are explored. Mild conditions are imposed on the triangulations which prevent them from deterioration and at the ...
-
Article
Atomic and Molecular Decomposition of Homogeneous Spaces of Distributions Associated to Non-negative Self-Adjoint Operators
Georgiadis, A. G.; Kerkyacharian, G.; Kyriazis, George; Petrushev, P. (2019)We deal with homogeneous Besov and Triebel–Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov ...
-
Article
Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators
Dekel, S.; Kerkyacharian, G.; Kyriazis, George C.; Petrushev, P. (2014)A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure ...
-
Article
"Compactly" supported frames for spaces of distributions on the ball
Kyriazis, George C.; Petrushev, P. (2012)
-
Article
Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
Kyriazis, George C.; Petrushev, P.; Xu, Y. (2008)Weighted Triebel-Lizorkin and Besov spaces on the unit ball Bd in d with weights wμ(x)=(1-x2)μ-1/2, μ≥0, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial ...
-
Article
Hardy spaces associated with non-negative self-adjoint operators
Dekel, S.; Kerkyacharian, G.; Kyriazis, George C.; Petrushev, P. (2017)The maximal and atomic Hardy spaces Hp and HA p, 0 < p ≤ 1, are considered in the setting of a doubling metric measure space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization. ...
-
Article
Homogeneous Besov and Triebel–Lizorkin spaces associated to non-negative self-adjoint operators
Georgiadis, Athanasios G.; Kerkyacharian, G.; Kyriazis, George C.; Petrushev, P. (2017)Homogeneous Besov and Triebel–Lizorkin spaces with complete set of indices are introduced in the general setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel ...
-
Article
Inversion of noisy Radon transform by SVD based needlets
Kerkyacharian, G.; Kyriazis, George C.; Le Pennec, E.; Petrushev, P.; Picard, D. (2010)A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the ...
-
Article
Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces
Kyriazis, George C.; Petrushev, P.; Xu, Y. (2008)The Littlewood-Paley theory is extended to weighted spaces of distributions on [-1,1] with Jacobi weights w(t) = (1 - t)α(1+t) β. Almost exponentially localized polynomial elements (needlets) {ρξ}, {ψξ} are constructed ...
-
Article
New bases for Triebel-Lizorkin and Besov spaces
Kyriazis, George C.; Petrushev, P. (2002)We give a new method for construction of unconditional bases for general classes of Triebel-Lizorkin and Besov spaces. These include the Lp, Hp, potential, and Sobolev spaces. The main feature of our method is that the ...
-
Conference Object
A new proof of the atomic decomposition of Hardy spaces
Dekel, S.; Kerkyacharian, G.; Kyriazis, George; Petrushev, P. (Marin Drinov Academic Publishing House, 2018)
-
Article
On the construction of frames for spaces of distributions
Kyriazis, George C.; Petrushev, P. (2009)We introduce a new method for constructing frames for general distribution spaces and employ it to the construction of frames for Triebel-Lizorkin and Besov spaces on the sphere. Conceptually, our scheme allows the freedom ...
-
Article
On the construction of frames for Triebel-Lizorkin and Besov spaces
Kyriazis, George C.; Petrushev, P. (2006)We present a general method for construction of frames {ψ I} I∈D for Triebel-Lizorkin and Besov spaces, whose nature can be prescribed. In particular, our method allows for constructing frames consisting of rational functions ...
-
Article
Rational bases for spaces of holomorphic functions in the disc
Kyriazis, George C.; Petrushev, P. (2014)A new method for construction of bases for general distribution spaces is developed. This method allows the freedom to prescribe the nature and properties of the basis elements. The method is deployed to the construction ...
-
Article
Rational bases for spaces of holomorphic functions in the disc
Kyriazis, George C.; Petrushev, P. (2014)