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01/26/06 Colloquium
Dr. Dorin Dutkay
Rutgers University
Rutgers University
Wavelets and self-similarity
Abstract: In the past twenty years the theory of wavelets has proved to be extremely successful, with important applications to image compression and signal processing. The theory involves the construction of orthonormal bases in euclidian spaces generated by translations and dilations. A key feature of these constructions is the property of self-similarity. We exploit this property and, using operator algebra methods, we offer a wider perspective on the subject. We show how techniques from the theory of wavelets can be used in many other contexts such as fractals, dynamical systems, or endomorphisms of von Neumann algebras. Thus, we can construct rich multiresolution structures with scaling functions and wavelets on fractals, solenoids, super-wavelets for Hilbert spaces containing L2(R), or harmonic bases on fractal measures.