On the construction of frames for spaces of distributions

DOI10.1016/j.jfa.2009.06.030zbMath1179.42025OpenAlexW2050340614MaRDI QIDQ837076

George C. Kyriazis, Pencho P. Petrushev

Publication date: 10 September 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.06.030

zbMATH Keywords

perturbationsframesBesov spaces on the spherespaces of distributionsTriebel-Lizorkin spaces on the sphere

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) General harmonic expansions, frames (42C15) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Inner product spaces and their generalizations, Hilbert spaces (46C99)

Related Items

Wavelet transforms for homogeneous mixed-norm Triebel-Lizorkin spaces ⋮ Discrete decomposition of homogeneous mixed-norm Besov spaces ⋮ Riesz-Fischer maps, semi-frames and frames in rigged Hilbert spaces ⋮ Rational bases for spaces of holomorphic functions in the disc ⋮ Distribution frames and bases ⋮ Nonlinear $n$-term approximation of harmonic functions from shifts of the Newtonian kernel ⋮ ``Compactly supported frames for spaces of distributions on the ball

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A discrete transform and decompositions of distribution spaces
• Decomposition of Besov and Triebel-Lizorkin spaces on the sphere
• Intrinsic localization of frames
• Decomposition of spaces of distributions induced by Hermite expansions
• Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions
• Bases consisting of rational functions of uniformly bounded degrees or more general functions
• Localized frames are finite unions of Riesz sequences
• Localization of frames, Banach frames, and the invertibility of the frame operator
• Localized polynomial frames on the ball
• Localized polynomial frames on the interval with Jacobi weights
• New bases for Triebel-Lizorkin and Besov spaces
• On the construction of frames for Triebel-Lizorkin and Besov spaces
• Localized Tight Frames on Spheres
• Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
• Perturbations of Banach Frames and Atomic Decompositions
• Continuous and Discrete Wavelet Transforms
• Jacobi decomposition of weighted Triebel–Lizorkin and Besov spaces
• A Class of Nonharmonic Fourier Series