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Frames, Bases and Group Representations

Deguang Han McMaster University, Hamilton, ON, Canada
David R. Larson Texas A & M University, College Station, TX
Available Formats:
Electronic ISBN: 978-1-4704-0288-4
Product Code: MEMO/147/697.E
List Price: $51.00 MAA Member Price:$45.90
AMS Member Price: $30.60 Click above image for expanded view Frames, Bases and Group Representations Deguang Han McMaster University, Hamilton, ON, Canada David R. Larson Texas A & M University, College Station, TX Available Formats:  Electronic ISBN: 978-1-4704-0288-4 Product Code: MEMO/147/697.E  List Price:$51.00 MAA Member Price: $45.90 AMS Member Price:$30.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1472000; 94 pp
MSC: Primary 46; 47; 42;

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.

• Chapters
• Introduction
• 1. Basic theory for frames
• 2. Complementary frames and disjointness
• 3. Frame vectors for unitary systems
• 4. Gabor type unitary systems
• 5. Frame wavelets, super-wavelets and frame sets
• 6. Frame representations for groups
• 7. Concluding remarks
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Volume: 1472000; 94 pp
MSC: Primary 46; 47; 42;

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.