# BRACKET PRODUCTS FOR WEYL-HEISENBERG FRAMES

@article{Casazza2003BRACKETPF, title={BRACKET PRODUCTS FOR WEYL-HEISENBERG FRAMES}, author={Peter G. Casazza and Mark Lammers}, journal={arXiv: Functional Analysis}, year={2003}, pages={71-98} }

We provide a detailed development of theL 1function-valued inner product onL 2(ℝ) known as the bracket product. In addition to some of the more basic properties, we show that this inner product has a Bessel’s inequality, a Riesz Representation Theorem, and a Gram—Schmidt process. We then apply this to Weyl—Heisenberg frames to show that there exist “compressed” versions of the frame operator, the frame transform and the preframe operator. Finally, we introduce the notion of an a-frame and show…

## 22 Citations

### ϕ-FACTORABLE OPERATORS AND WEYL-HEISENBERG FRAMES ON LCA GROUPS

- Mathematics
- 2011

We investigate '-factorable operators and Weyl-Heise- nberg frames with respect to a function-valued inner product, the so called '-bracket product on L 2 (G), where G is a locally compact abelian…

### N ov 1 99 9 ANALYZING THE WEYL-HEISENBERG FRAME IDENTITY

- Mathematics
- 2008

In 1990, Daubechies proved a fundamental identity for WeylHeisenberg systems which is now called the Weyl-Heisenberg Frame Identity. WH-Frame Identity: If g ∈ W (L∞, L), then for all continuous,…

### A characterization of L-dual frames and L-dual Riesz bases

- Mathematics
- 2011

This paper is an investigation of L-dual frames with respect to a function-valued inner product, the so called L-bracket product on L 2 (G), where G is a locally compact abelian group with a uniform…

### An Introduction to Irregular Weyl-Heisenberg Frames

- Mathematics
- 2004

An introduction to irregular Weyl-Heisenberg (WH) frames showing the latest developments and open problems and several new results for semi-irregular WH-frames are provided.

### Gabor Analysis, Noncommutative Tori and Feichtinger's Algebra

- Mathematics
- 2008

We point out a connection between Gabor analysis and noncommutative analysis. Especially, the strong Morita equivalence of noncommutative tori appears as underlying setting for Gabor analysis, since…

### Gabor Analysis, Noncommutative Tori and Feichtinger's algebra

- Mathematics
- 2005

We point out a connection between Gabor analysis and noncommutative analysis. Especially, the strong Morita equivalence of noncommutative tori appears as underlying setting for Gabor analysis, since…

### A new function-valued inner product and corresponding function-valued frames in L2 (0,∞)

- Mathematics
- 2014

In this paper for real number , we define a function-valued inner product on by using dilation operator. We consider the relationship between orthonormal sequences, orthonormal bases and frames…

### FRAMES IN HILBERT C*-MODULES AND C*-ALGEBRAS

- Mathematics
- 2002

We present a general approach to a module frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the ideas of geometric dilation to standard Hilbert C*-modules over unital…

### Wavelets and Hilbert Modules

- Mathematics
- 2004

AbstractA Hilbert C*-module is a generalization of a Hilbert space for which the inner
product takes its values in a C*-algebra instead of the complex numbers. We use the bracket
product to construct…

### Bracket products on Locally compact abelian groups

- Mathematics
- 2008

We define a new function-valued inner product on L 2 (G), called φ-bracket product, where G is a locally compact abelian group and φ is a topological isomorphism on G. We investigate the notion of…

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