scholarly journals Bessel Sequences and Affine Frames

1993 ◽  
Vol 1 (1) ◽  
pp. 29-49 ◽  
Author(s):  
Charles K. Chui ◽  
Xianliang Shi
Keyword(s):  
Affine Frames ◽  
Bessel Sequences

The Characterization of Orthogonal Affine Bivariate Pseudoframes

2010 ◽  
Vol 129-131 ◽  
pp. 33-37
Author(s):  
Qing Jiang Chen ◽  
Fang Lin
Keyword(s):  
Finite Number ◽  
Frame Theory ◽  
The Other ◽  
Constructive Method ◽  
Affine Frames ◽  
Bessel Sequences ◽  
Bivariate Functions

The frame theory has been one of powerful tools for researching into wavelets. The notion of the bivariate generalized multiresolution structure (BGMS) is presented. The concepts of Bessel sequences and orthogonal bivariate pseudoframes are introduced. Two Bessel sequences are said to be orthogonal ones if the composition of synthesis operator of one sequence with the analysis operator of the other is the zero-operator. It is characterized that when two Bessel sequences are orthogonal while the Bessel sequences possess the form of translates of a finite number of bivariate functions in . A constructive method for affine frames of based on a BGMS is established.

New characterizations of g-frames and g-Riesz bases

2018 ◽  
Vol 16 (06) ◽  
pp. 1850053 ◽  
Author(s):  
Dongwei Li ◽  
Jinsong Leng ◽  
Tingzhu Huang
Keyword(s):  
Riesz Basis ◽  
Riesz Bases ◽  
Gram Matrix ◽  
Necessary Condition ◽  
Topological Properties ◽  
Bessel Sequence ◽  
Bessel Sequences ◽  
Sufficient And Necessary Condition

In this paper, we give some new characterizations of g-frames, g-Bessel sequences and g-Riesz bases from their topological properties. By using the Gram matrix associated with the g-Bessel sequence, we present a sufficient and necessary condition under which the sequence is a g-Bessel sequence (or g-Riesz basis). Finally, we consider the excess of a g-frame and obtain some new results.

scholarly journals A New Inequality for Frames in Hilbert Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Zhong-Qi Xiang
Keyword(s):  
Linear Operator ◽  
Hilbert Spaces ◽  
Bounded Linear Operator ◽  
Bounded Linear ◽  
Bessel Sequences

We obtain a new inequality for frames in Hilbert spaces associated with a scalar and a bounded linear operator induced by two Bessel sequences. It turns out that the corresponding results due to Balan et al. and Găvruţa can be deduced from our result.

scholarly journals Affine frames, GMRA's, and the canonical dual

2003 ◽  
Vol 159 (3) ◽  
pp. 453-479 ◽  
Author(s):  
Marcin Bownik ◽  
Eric Weber
Keyword(s):  
Affine Frames

scholarly journals Controlled G-Frames and Their G-Multipliers in Hilbert spaces

2013 ◽  
Vol 21 (2) ◽  
pp. 223-236 ◽  
Author(s):  
Asghar Rahimi ◽  
Abolhassan Fereydooni
Keyword(s):  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Multiplier Operator ◽  
Frame Operator ◽  
Fixed Sequence ◽  
Numerical Efficiency ◽  
Bessel Sequences ◽  
Almost All

Abstract Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are opera- tors that combine (frame-like) analysis, a multiplication with a fixed sequence ( called the symbol) and synthesis. One of the last extensions of frames is weighted and controlled frames that introduced by P.Balazs, J-P. Antoine and A. Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Also g-frames are the most popular generalization of frames that include almost all of the frame extensions. In this manuscript the concept of the controlled g- frames will be defined and we will show that controlled g-frames are equivalent to g-frames and so the controlled operators C and C' can be used as preconditions in applications. Also the multiplier operator for this family of operators will be introduced and some of its properties will be shown.

scholarly journals Multipliers for p-Bessel Sequences in Banach Spaces

2010 ◽  
Vol 68 (2) ◽  
pp. 193-205 ◽  
Author(s):  
Asghar Rahimi ◽  
Peter Balazs
Keyword(s):  
Banach Spaces ◽  
Bessel Sequences

scholarly journals Invertibility of multipliers in Hilbert C*-modules

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6073-6085
Author(s):  
Azandaryania Mirzaee
Keyword(s):  
Sufficient Conditions ◽  
Riesz Bases ◽  
Small Perturbations ◽  
Bessel Sequences ◽  
Bessel Multipliers

In this paper, we present some sufficient conditions under which Bessel multipliers in Hilbert C*-modules with semi-normalized symbols are invertible and we calculate the inverses. Especially we consider the invertibility of Bessel multipliers when the elements of their symbols are positive and when their Bessel sequences are equivalent, duals, modular Riesz bases or stable under small perturbations. We show that in these cases the inverse of a Bessel multiplier can be represented as a Bessel multiplier.

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