Frames for operators
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TL;DR: In this article, a generalization of frames in Hilbert spaces is presented, which allows, in a stable way, to reconstruct elements from the range of a linear and bounded operator in a Hilbert space.
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About: This article is published in Applied and Computational Harmonic Analysis. The article was published on 01 Jan 2012. and is currently open access. The article focuses on the topics: Operator space & Hilbert space.
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Citations
Canonical dual K-Bessel sequences and dual K-Bessel generators for unitary systems of Hilbert spaces
TL;DR: In this article, the concept of canonical dual K-Bessel sequences of a K-frame was introduced and a simple way to construct new K-frames from given ones was given.
41
Generalized frames for operators in Hilbert spaces
TL;DR: In this paper, a family of analysis and synthesis systems of operators with frame-like properties for the range of a bounded operator on a separable Hilbert space is presented, called a Θ-g-frame.
38
Weaving K -Frames in Hilbert Spaces
Deepshikha,Lalit Kumar Vashisht +1 more
TL;DR: In this article, necessary and sufficient conditions for weaving K-frames in Hilbert spaces are presented, where the Paley-Wiener type perturbation of K-frame is considered.
34
G-frames with bounded linear operators
TL;DR: In this article, the authors introduce the more general g-frame which is called a $K$-g-frame by combining a gframe with a bounded linear operator in a Hilbert space.
Weaving K-frames in Hilbert Spaces
Deepshikha,Lalit Kumar Vashisht +1 more
TL;DR: In this article, the necessary and sufficient conditions for weaving K-frames in Hilbert spaces were presented, and sufficient condition for Paley-Wiener type perturbation of weaving k-frames were given.
28
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Ole Christensen
- 13 Dec 2002
TL;DR: In this article, a generalized Shift-Invariant Systems in L2(Rd) is proposed for Gabor Frames in L 2(Z),L 2(0,L),CL.
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Ronald G. Douglas
- 01 Feb 1966
TL;DR: In this paper, it was shown that a close relationship exists between the notions of majorization, factorization, and range inclusion for operators on a Hilbert space, and that these notions fit together to yield theorems.