Continuous Atomic Systems for Subspaces

Javanshiri, Hossein; Fattahi, A.

doi:10.1007/s00009-015-0593-4

Cited by 10 publications

(4 citation statements)

References 41 publications

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“…Specifically, reconstruction of the original vector from frame is typically achieved by using a so-called duality notion. A number of variations and generalizations of duality notion can be found in Li and Ogawa 2,3 in the more general context of pseudo-duality, atomic system for subspace, 4,5 approximate duality, 6,7 and generalized duality. [7][8][9] In many situations, it is important to know which properties of frames are stable if we slightly modify the elements of the systems.…”

Section: Introductionmentioning

confidence: 99%

The effect of perturbations of frames on their alternate and approximately dual frames

Javanshiri

Hajiabootorabi

Mardanbeigi

2021

Math Methods in App Sciences

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Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory, and sensor modeling. In recent years, the computing of the associated deviations of the canonical and alternate dual frames from the original ones has been considered by functional analysts. In this paper, we consider the quantitative measurement of the associated deviations of the alternate and approximately dual frames from the original ones. More precisely, it is proved that if the sequence Ψ is sufficiently close to the frame Φ, then for given approximately dual frame Φ ad of Φ, the approximately dual frame Ψ ad of Ψ can be found which is close to Φ ad , and particularly, we estimate their deviation in terms of the distance of the operators  1 ∶= T Φ U Φ ad and  2 ∶= T Ψ U Ψ ad and their approximation rates, where T X and U X denote the synthesis and analysis operators of the frame X, respectively. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literatures on this topic.

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Section: Introductionmentioning

confidence: 99%

The effect of perturbations of frames on their alternate and approximately dual frames

Javanshiri

Hajiabootorabi

Mardanbeigi

2021

Math Methods in App Sciences

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“…In recent years there has been shown considerable interest by functional analysts in the study of Bessel multipliers as a generalization of the frame operators, approximately dual frames [7], generalized dual frames [7,Remark 2.8(ii)] and atomic systems for subspaces [10]. In fact, the study of this class of operators leads us to new results concerning dual frames and local atoms, two concepts at the core of frame theory.…”

Section: Introductionmentioning

confidence: 99%

Invertibility of generalized g-frame multipliers in Hilbert spaces

Abolghasemi¹,

Tolooei²,

Moosavianfard³

2019

Preprint

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In this paper, we investigate the invertibility of generalized g-Bessel multipliers. We show that for semi-normalized symbols, the inverse of any invertible generalized g-frame multiplier can be represented as a generalized g-frame multiplier. Also we give several approaches for constructing invertible generalized g-frame multipliers from the given one. It is worth mentioning that some of our results are quite different from those studied in the previous literatures on this topic. 2010 MSC : 42C15, 47A05, 41A58.

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“…We also recall that by the spectral theorem, every self-adjoint compact operator on a Hilbert space can be represented as a multiplier using an orthonormal system. In addition to all these, multipliers generalize the frame operators, approximately dual frames [8,20], generalized dual frames [20,Remark 2.8(ii)], atomic systems for subspaces [16,21] and frames for operators [18]. Therefore, the study of Bessel multipliers also leads us to new results concerning dual frames and local atoms, two concepts at the core of frame theory.…”

Section: Introductionmentioning

confidence: 99%

Multipliers for von Neumann–Schatten Bessel sequences in separable Banach spaces

Javanshiri

Choubin

2018

Linear Algebra and its Applications

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In this paper we introduce the concept of von Neumann-Schatten Bessel multipliers in separable Banach spaces and obtain some of their properties. Finally, special attention is devoted to the study of invertible Hilbert-Schmidt frame multipliers. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for diagonalization of matrices in finite dimensional setting as well as for dual HS-frames.In particular, we show that a HS-frame is uniquely determined by the set of its dual HS-frames.2010 Mathematics Subject Classification. Primary 46C50, 65F15, 42C15; Secondary 41A58, 47A58.

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Continuous Atomic Systems for Subspaces

Cited by 10 publications

References 41 publications

The effect of perturbations of frames on their alternate and approximately dual frames

The effect of perturbations of frames on their alternate and approximately dual frames

Invertibility of generalized g-frame multipliers in Hilbert spaces

Multipliers for von Neumann–Schatten Bessel sequences in separable Banach spaces

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