Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators

S. Dekel, et al. "Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators." Studia Mathematica 225.2 (2014): 115-163. <http://eudml.org/doc/285778>.

@article{S2014,
abstract = {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 space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with Jacobi weights as well as on Lie groups, Riemannian manifolds, and in various other settings. The compactly supported frames are utilized to introduce atomic Hardy spaces $H^\{p\}_\{A\}$ in the general setting of this article.},
author = {S. Dekel, G. Kerkyacharian, G. Kyriazis, P. Petrushev},
journal = {Studia Mathematica},
keywords = {heat kernel; frames; Besov spaces; Triebel-Lizorkin spaces; Hardy spaces},
language = {eng},
number = {2},
pages = {115-163},
title = {Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators},
url = {http://eudml.org/doc/285778},
volume = {225},
year = {2014},
}

TY - JOUR
AU - S. Dekel
AU - G. Kerkyacharian
AU - G. Kyriazis
AU - P. Petrushev
TI - Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators
JO - Studia Mathematica
PY - 2014
VL - 225
IS - 2
SP - 115
EP - 163
AB - 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 space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with Jacobi weights as well as on Lie groups, Riemannian manifolds, and in various other settings. The compactly supported frames are utilized to introduce atomic Hardy spaces $H^{p}_{A}$ in the general setting of this article.
LA - eng
KW - heat kernel; frames; Besov spaces; Triebel-Lizorkin spaces; Hardy spaces
UR - http://eudml.org/doc/285778
ER -