Frames, Semi-Frames, and Hilbert Scales

DOI10.1080/01630563.2012.682128zbMath1255.42024arXiv1203.0506OpenAlexW2040884834WikidataQ58232590 ScholiaQ58232590MaRDI QIDQ2919976

Peter Balazs, Jean-Pierre Antoine

Publication date: 23 October 2012

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.0506

zbMATH Keywords

framesfusion framesHilbert scalessemi-frames

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Generalizations of inner products (semi-inner products, partial inner products, etc.) (46C50) Numerical methods for wavelets (65T60) General harmonic expansions, frames (42C15) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items (14)

Reproducing pairs and the continuous nonstationary Gabor transform on LCA groups ⋮ \(U\)-cross Gram matrices and their invertibility ⋮ Reproducing pairs of measurable functions ⋮ Frames and weak frames for unbounded operators ⋮ Generalized frame operator, lower semiframes, and sequences of translates ⋮ Lower semi-frames, frames, and metric operators ⋮ Frames for the Solution of Operator Equations in Hilbert Spaces with Fixed Dual Pairing ⋮ Biorthogonal vectors, sesquilinear forms, and some physical operators ⋮ Reproducing pairs of measurable functions and partial inner product spaces ⋮ Reproducing pairs and Gabor systems at critical density ⋮ Operators on partial inner product spaces: towards a spectral analysis ⋮ PIP-space valued reproducing pairs of measurable functions ⋮ Sesquilinear forms associated to sequences on Hilbert spaces ⋮ Frames, their relatives and reproducing kernel Hilbert spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Invertibility of multipliers
• Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products
• Frame expansions in separable Banach spaces
• Series expansions in Fréchet spaces and their duals, construction of Fréchet frames
• Continuous frames, function spaces, and the discretization problem
• Intrinsic localization of frames
• Fusion frames and distributed processing
• On the properties of generalized frames
• Partial inner product spaces. Theory and applications
• Partial inner product spaces and semi-inner product spaces
• Continuous frames in Hilbert space
• Frames associated with measurable spaces
• Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for \(L^2(\mathbb R{^d})\)
• Frames and pseudo-inverses
• Some examples of normed Köthe spaces
• \(g\)-frames and \(g\)-Riesz bases
• Multipliers for continuous frames in Hilbert spaces
• Painless nonorthogonal expansions
• Ten Lectures on Wavelets
• WEIGHTED AND CONTROLLED FRAMES: MUTUAL RELATIONSHIP AND FIRST NUMERICAL PROPERTIES
• Distributions and Their Hermite Expansions
• An introduction to frames and Riesz bases
• \(p\)-frames and shift invariant subspaces of \(L^p\)

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