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VIGRE seminar, fall 2000: Problems in Matrix Analysis and
Wavelet Theory
 Instructors
 David Larson, Eric Weber
 Students enrolled
 Scott Armstrong, Vincent Lemoine (undergraduate mathematics
students); Scott Evans (undergraduate physics student); Eric
Bahuaud, Troy Henderson, AliAmir Husain, Quoc Le Gia, Lovas
Randrianarivony, Darren Rhea, Xiaofei Zhang (graduate mathematics
students)
 Description
 The interplay between operator theory and wavelet theory has
produced deep, rich results. We investigated the role of wandering
vectors for unitary systems, both in finite and infinite
dimensions. Related topics include introductory ideas in operator
algebras, again both in finite and infinite dimensions. In
addition, we studied minimally supported frequency wavelets. This
special class of wavelets has an interesting internal structure,
but also provides concrete examples of important ideas that were
discussed. Finally, we investigated several interesting intrinsic
problems dealing with wavelet sets.
 Examples of Research Problems

 Open problems regarding wandering vectors for unitary systems
acting on R^{n} or C^{n}.
 An open problem on the reflexivity of finite dimensional
operator algebras which is purely algebraic in nature.
 Characterize interpolation pairs of minimally supported
frequency wavelets.
 How can a wavelet set be perturbed to give rise to an
interpolation pair?
 Does there exist a wavelet set in the support of the Fourier
transform of any wavelet?