An introduction to frames and Riesz bases

By Ole W. Christensen. 2002

3,278 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/13af207e2ab3c2dc3c74e909fb05040ed1b6bb46

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In Applied Mathematics

Citations in the corpus

Frames of subspaces (2003, methodology): “Christensen,An introduction to fram es and Riesz bases,Birkh auser,Boston,2003.”
Abstract Harmonic Analysis of Continuous Wavelet Transforms (2005, background): “By now there exists extensive literature concerning the construction of wavelet frames and related constructions such as Gabor frames, see the monograph [28] and the references therein.”
Resolution of the wavefront set using continuous shearlets (2006, background): “We refer the reader to [8, 9] for more details about frames.”
On the construction of equiangular frames from graphs (2009, background): “The basic theory of finite frames The following definitions and observations are well known (cf [C03], [W09]).”
Operator-valued frames (2007, background): “Important examples of infinite frames are the Gabor (Weyl-Heisenberg) frames of time-frequency analysis and the wavelet frames [7].”
Dynamical sampling and frame representations with bounded operators (2018, background): “The result now follows from the perturbation results in [9, 10] (or [6], page 565).”
Error bounds for kernel-based approximations of the Koopman operator (2023, background): “In this section, let H be a Hilbert space.”
Duality Principles in Frame Theory (2004, methodology): “For more information we refer to the excellent survey articles by Casazza [3, 2], the recognized books by Christensen [5], Gröchenig [11], and Young [17] and the very well written research-tutorial by Heil and Walnut [13].”
Tight informationally complete quantum measurements (2006, background): “A weighted 1design is known as a tight (vector) frame in the context of frame theory [20, 21, 22], in which case the unnormalized states |x̃〉 ≡ √ w(x)d |x〉 are the frame vectors, and Eq.”
G-frames and G-Riesz Bases (2005, methodology): “We refer to [4, 7, 11, 14, 15, 16, 20] for an introduction to the frame theory and its applications.”
On Fourier frame of absolutely continuous measures (2011, background): “One may refer to [1] and [9] for some excellent expositions.”
Localization of frames II (2004, background): “For up-to-date treatments of frames one may consult the monographs [4, 5 , 29] or the special issue [2].”
Quasi-probability representations of quantum theory with applications to quantum information science (2010, background): “A frame can be thought of as a generalization of an orthonormal basis (Christensen, 2003).”