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Frames, Bases and Group Representations
Deguang Han, McMaster University, Hamilton, ON, Canada, and David R. Larson, Texas A & M University, College Station, TX

Memoirs of the American Mathematical Society
2000; 94 pp; softcover
Volume: 147
ISBN-10: 0-8218-2067-2
ISBN-13: 978-0-8218-2067-4
List Price: US$51
Individual Members: US$30.60
Institutional Members: US$40.80
Order Code: MEMO/147/697
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We develop an operator-theoretic approach to discrete frame theory on a separable Hilbert space. We then apply this to an investigation of the structural properties of systems of unitary operators on Hilbert space which are related to orthonormal wavelet theory. We also obtain applications of frame theory to group representations, and of the theory of abstract unitary systems to frames generated by Gabor type systems.


Graduate students and research mathematicians interested in functional analysis.

Table of Contents

  • Introduction
  • Basic theory for frames
  • Complementary frames and disjointness
  • Frame vectors for unitary systems
  • Gabor type unitary systems
  • Frame wavelets, super-wavelets and frame sets
  • Frame representations for groups
  • Concluding remarks
  • Bibliography
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