Uniform Excess Frames in Hilbert Spaces

Xiao, Xiangchun; Zhou, Guorong; Zhu, Yixin

doi:10.1007/s00025-018-0871-0

Cited by 6 publications

(2 citation statements)

References 17 publications

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“…Remark 3. Inequalities (16) and (17) in Corollary 4 are respectively inequalities in Theorems 14 and 15 shown in [36].…”

Section: Corollarymentioning

confidence: 94%

“…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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“…Remark 3. Inequalities (16) and (17) in Corollary 4 are respectively inequalities in Theorems 14 and 15 shown in [36].…”

Section: Corollarymentioning

confidence: 94%