BRACKET PRODUCTS FOR WEYL-HEISENBERG FRAMES

@article{Casazza1999BRACKETPF,
  title={BRACKET PRODUCTS FOR WEYL-HEISENBERG FRAMES},
  author={Peter G. Casazza and Mark Lammers},
  journal={arXiv: Functional Analysis},
  year={1999},
  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… 

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