More on Inequalities for Weaving Frames in Hilbert Spaces
Open Access
- 2 February 2019
- journal article
- research article
- Published by MDPI AG in Mathematics
- Vol. 7 (2) , 141
- https://doi.org/10.3390/math7020141
Abstract
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.Keywords
Funding Information
- National Natural Science Foundation of China (11761057 and 11561057)
This publication has 32 references indexed in Scilit:
- Invertibility and robustness of phaseless reconstructionApplied and Computational Harmonic Analysis, 2015
- Reconstruction of Signals From Frame Coefficients With Erasures at Unknown LocationsIEEE Transactions on Information Theory, 2014
- Asymptotic properties of Gabor frame operators as sampling density tends to infinityJournal of Functional Analysis, 2010
- A new identity for Parseval framesProceedings of the American Mathematical Society, 2007
- Spectrally two-uniform frames for erasuresOperators and Matrices, 2007
- On some identities and inequalities for frames in Hilbert spacesJournal of Mathematical Analysis and Applications, 2006
- On signal reconstruction without phaseApplied and Computational Harmonic Analysis, 2006
- Grassmannian frames with applications to coding and communicationApplied and Computational Harmonic Analysis, 2003
- Painless nonorthogonal expansionsJournal of Mathematical Physics, 1986
- A class of nonharmonic Fourier seriesTransactions of the American Mathematical Society, 1952