Unconditional Convergence for Wavelet Frame Expansions

2018 ◽  
Vol 234 (3) ◽  
pp. 357-361
Author(s):  
E. A. Lebedeva
Keyword(s):  
Unconditional Convergence ◽  
Wavelet Frame ◽  
Frame Expansions

scholarly journals Two Banach spaces of atoms for stable wavelet frame expansions

2007 ◽  
Vol 146 (1) ◽  
pp. 28-70 ◽  
Author(s):  
Hans G. Feichtinger ◽  
Wenchang Sun ◽  
Xingwei Zhou
Keyword(s):  
Banach Spaces ◽  
Wavelet Frame ◽  
Frame Expansions

Unconditional convergence constants of g-frame expansions

2020 ◽  
Vol 18 (04) ◽  
pp. 2050022
Author(s):  
Dongwei Li
Keyword(s):  
Hilbert Space ◽  
Unconditional Convergence ◽  
Tight Frames ◽  
Bessel Sequence ◽  
Frame Bounds ◽  
Frame Expansion ◽  
The Cross ◽  
Frame Expansions ◽  
Uniformly Bounded

In this paper, we prove that the unconditional constants of the g-frame expansion in a Hilbert space are bounded by [Formula: see text], where [Formula: see text], [Formula: see text] are the frame bounds of the g-frames. It follows that tight g-frames have unconditional constant one. Then we generalize this to a classification of such g-frames by showing that a g-Bessel sequence has unconditional constant one if it is an orthogonal sum of g-tight frames. We also obtain a new result under which a g-Bessel sequence is a g-frame from the view of unconditional constant. Finally, we prove similar results for cross g-frame expansions as long as the cross g-frame expansions stay uniformly bounded away from zero.

Properties of frames and relationships between them with emphasis on subframes and unconditional convergence

2016 ◽  
Author(s):  
◽  
Travis Bemrose
Keyword(s):  
Unconditional Convergence ◽  
University Of Missouri ◽  
The University

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.]

On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle

2014 ◽  
Vol 57 (2) ◽  
pp. 254-263 ◽  
Author(s):  
Ole Christensen ◽  
Hong Oh Kim ◽  
Rae Young Kim
Keyword(s):  
Extension Principle ◽  
Sufficient Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Number Of Generators ◽  
Unitary Extension

AbstractThe unitary extension principle (UEP) by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the UEP-type wavelet systems that can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible.

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