Results 1 to 10 of about 86,604 (155)
Archiv Der Mathematik, 2014 The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogous to the canonical dual frame. Here a new concept of dual is studied in infinite-dimensional separable Hilbert spaces. It extends the commonly used notion and overcomes these technical difficulties. We
Heineken, Sigrid Bettina +3 more
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Journal of Mathematical Analysis and Applications, 2008 The authors study generalized, i.e., \(g\)-frames in a Hilbert space \(U\), that is, sequences \((\Lambda_i)_{i\in I}\) of linear operators \(\Lambda_i:U\to V_i\) such that \[ A\| f\| ^2 \leq \sum_{i\in I} \| \Lambda_i f\| ^2 \leq B \| f\| ^2, \] for some positive constants \(A\) and \(B\).
Amir Khosravi
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The Structure of Minimizers of the Frame Potential on Fusion Frames [PDF]
Journal of Fourier Analysis and Applications, 2009 In this paper we study the fusion frame potential, that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. The structure of local and global minimizers of this potential is studied, when we restrict the frame potential to suitable sets of fusion frames. These minimizers are related to
Pedro Massey +2 more
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Oblique Dual Fusion Frames [PDF]
Numerical Functional Analysis and Optimization, 2018 We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space and under certain consistency requirements, are analyzed in one subspace and are reconstructed in another subspace.
Heineken, Sigrid Bettina +1 more
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Fusion frames and G-frames in Banach spaces
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Behrooz Khosravi +2 more
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A note on perturbations of fusion frames [PDF]
Journal of Mathematical Analysis and Applications, 2018 In this work, we consider some relationships between a closed range operator $T$ and a fusion frame $\mathcal{W}=(W_i,w_i)_{i\in I}$ for a Hilbert space $\mathcal{H}$ that provides that the sequence $(\overline{T(W_i)},v_i)_{i\in I}$ is a fusion frame sequence for $\mathcal{H}$, if we consider a suitable family of weights $\{v_i\}_{i\in I}$.
Calderón, Pablo Luis +1 more
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Applied and Computational Harmonic Analysis, 2013 Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion frames. Tight p-fusion frames are closely related to the classical notions of designs and cubature formulas in Grassmann spaces and are analyzed with methods from harmonic ...
Bachoc, Christine, Ehler, Martin
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Fusion frames and distributed processing
Applied and Computational Harmonic Analysis, 2008 Let $\{W_i\}_{i\in I}$ be a (redundant) sequence of subspaces each being endowed with a weight $v_i$, and let $\mathcal{H}$ be the closed linear span of the $W_i$'s, a composite Hilbert space. Provided that $\{(W_i,v_i)\}_{i \in I}$ satisfies a certain property which controls the weighted overlaps of the subspaces, it is called a {\em fusion frame ...
Peter Casazza, Gitta Kutyniok
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New characterizations of fusion frames (frames of subspaces)
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2009 This work gives new characterizations of fusion frames, studies the behavior of fusion frames under bounded operators with closed range, and erasures of subspaces of fusion frames. It also shows that every fusion frame is the image of an orthonormal fusion basis under a bounded surjective operator.
Mohammad Sadegh Asgari
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Construction of continuous $g$-frames and continuous fusion frames [PDF]
Sahand Communications in Mathematical Analysis, 2016 A generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by M. H. Faroughi and R. Ahmadi, is presented in this study. Continuous resolution of the identity (CRI) is introduced, a new family of
Mahdiyeh Khayyami, Akbar Nazari
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