Norm Retrievable Frames in $\mathbb{R}^n$

Fard, M. A. Hasankhani

doi:10.13001/1081-3810.3260

Cited by 10 publications

(11 citation statements)

References 14 publications

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“…Let H = {h j } j∈J be the same as in the proof of Corollary 2. By combining Equations (10) and (12), and Theorem 2 we arrive at…”

Section: Corollarymentioning

confidence: 99%

“…The appearance of frames can be tracked back to the early 1950s when they were used in the work on nonharmonic Fourier series owing to Duffin and Schaeffer [1]. We refer to [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] for more information on general frame theory. It should be pointed out that frames have played an important role such as in signal processing [17,18], sigma-delta quantization [19], quantum information [20], coding theory [21], and sampling theory [22], due to their nice properties.…”

Section: Introductionmentioning

confidence: 99%

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More on Inequalities for Weaving Frames in Hilbert Spaces

Xiang

2019

Mathematics

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In this paper, we present several new inequalities for weaving frames in Hilbert spaces from the point of view of operator theory, which are related to a linear bounded operator induced by three Bessel sequences and a scalar in the set of real numbers. It is indicated that our results are more general and cover the corresponding results recently obtained by Li and Leng. We also give a triangle inequality for weaving frames in Hilbert spaces, which is structurally different from previous ones.

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“…Let H = {h j } j∈J be the same as in the proof of Corollary 2. By combining Equations (10) and (12), and Theorem 2 we arrive at…”

Section: Corollarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

More on Inequalities for Weaving Frames in Hilbert Spaces

Xiang

2019

Mathematics

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“…The following theorem in [13] uses the span of the frame elements to classify norm retrievable frames in R N . …”

Section: Classification Of Norm Retrievalmentioning

confidence: 99%

Norm Retrieval and Phase Retrieval by Projections

Casazza

Ghoreishi

Jose

et al. 2017

Axioms

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“…The following theorem in [22] uses the span of the frame elements to classify norm retrievable frames in R m .…”

Section: Classification Of Norm Retrievalmentioning

confidence: 99%

“…Theorem 2.0.32. [22] A frame {φ i } n i=1 ⊂ R m does norm retrieval if and only if for any partition…”

Section: Classification Of Norm Retrievalmentioning

confidence: 99%

Phase retrieval in frame theory

Ghoreishi¹

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This dissertation is the study of phase retrieval in frame theory. The first part is concerned with the analysis of phase retrieval and the complete classification of norm retrieval. Norm retrieval is essential to transfer the properties of phase retrieval to the complement space. The first section includes the results regarding projections and also the characterization of phase retrieval and norm retrieval for subspaces. The second part is the study of weak phase retrieval which was motivated by the idea of reducing the number of vectors satisfying the properties close to phase retrieval. The last section provides the correlation between weak phase retrieval and phase retrieval properties along with the examples illustrating the relationship between weak phase retrieval and the related concepts.

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Norm Retrievable Frames in $\mathbb{R}^n$

Cited by 10 publications

References 14 publications

More on Inequalities for Weaving Frames in Hilbert Spaces

More on Inequalities for Weaving Frames in Hilbert Spaces

Norm Retrieval and Phase Retrieval by Projections

Phase retrieval in frame theory

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