Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products

DOI10.1016/j.acha.2010.09.007zbMath1221.42067OpenAlexW1988936067MaRDI QIDQ544035

Haizhang Zhang, Jun Zhang

Publication date: 14 June 2011

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2010.09.007

zbMATH Keywords

waveletsBanach spacesHilbert spacesreproducing kernel Hilbert spacesframesRiesz basesBessel sequencessemi-inner productsreproducing kernel Banach spacesRiesz-Fischer sequencesShannon's sampling expansions

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Summability and bases in topological vector spaces (46A35) Lacunary series of trigonometric and other functions; Riesz products (42A55)

Related Items (25)

Optimal sampling points in reproducing kernel Hilbert spaces ⋮ Continuous framings for Banach spaces ⋮ Sampling Theory and Reproducing Kernel Hilbert Spaces ⋮ Frames, Semi-Frames, and Hilbert Scales ⋮ A converse sampling theorem in reproducing kernel Banach spaces ⋮ Sampling in reproducing kernel Banach spaces ⋮ On reproducing kernel Banach spaces: generic definitions and unified framework of constructions ⋮ Frames for operators in Banach spaces ⋮ Sparse machine learning in Banach spaces ⋮ \((X_d,x_d^\ast)\)-Bessel multipliers in Banach spaces ⋮ Separability of reproducing kernel spaces ⋮ Semi-frames and Fusion Semi-frames ⋮ Bessel Sequences and Frames in Semi-inner Product Spaces ⋮ Dilations of operator-valued measures with bounded \(p\)-variations and framings on Banach spaces ⋮ Multi-task learning in vector-valued reproducing kernel Banach spaces with the \(\ell^1\) norm ⋮ ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES ⋮ The Kramer sampling theorem revisited ⋮ Average sampling and reconstruction in a reproducing kernel subspace of homogeneous type space ⋮ Generalized framing and Riesz-dual sequences in Banach spaces ⋮ Existence of frames based on the Szegö kernel in the Hardy space ⋮ Frames in Semi-inner Product Spaces ⋮ Reproducing Kernel Banach Spaces with the ℓ¹ Norm II: Error Analysis for Regularized Least Square Regression ⋮ Signal representations via SIP p-frames and SIP Bessel multipliers in separable Banach spaces ⋮ Exponential approximation of multivariate bandlimited functions from average oversampling ⋮ SIP X_d-frames and their perturbations in uniformly convex Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Frame expansions in separable Banach spaces
• General sampling theorems for functions in reproducing kernel Hilbert spaces
• Generalized interpolating refinable function vectors
• Optimal learning of bandlimited functions from localized sampling
• On generalized adjoint Abelian operators on Banach spaces
• Describing functions: Atomic decompositions versus frames
• Representation of linear functionals in a Banach space
• Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's \((A_p)\) condition
• Sampling expansions and interpolation in unitarily translation invariant reproducing kernel Hilbert spaces
• \(p\)-frames in separable Banach spaces
• Nonharmonic analysis
• On the isometries of reflexive Orlicz spaces
• Shannon sampling. II: Connections to learning theory
• Generalized semi-inner products with applications to regularized learning
• On the mathematical foundations of learning
• Semi-Inner-Product Spaces
• Sampling Expansions in Reproducing Kernel Hilbert and Banach Spaces
• Characterizations of reflexivity
• Ten Lectures on Wavelets
• On linear independence for integer translates of a finite number of functions
• Shift-invariant spaces on the real line
• Sampling in the functional hilbert space induced by a hilbert space valued kernel
• Weighted Paley-Wiener spaces
• Shannon sampling and function reconstruction from point values
• A Generalized Sampling Theorem for Frequency Localized Signals
• On the localization and directionalization of uniform convexity
• Classes of Semi-Inner-Product Spaces
• Strictly Convex Spaces Via Semi-Inner-Product Space Orthogonality
• A Note on Some Operator Theory in Certain Semi-Inner-Product Spaces
• Theory of Reproducing Kernels
• A Class of Nonharmonic Fourier Series
• \(p\)-frames and shift invariant subspaces of \(L^p\)
• Functional analysis and infinite-dimensional geometry

This page was built for publication: Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products