Unitary matrix functions, wavelet algorithms, and structural properties of wavelets
Abstract
Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet constructions had previously been known, since Haar in 1910, it was the advent of multiresolutions, and subband filtering techniques which provided the tools for our ability to now easily create efficient algorithms, ready for a rich variety of applications to practical tasks. Part of the underpinning for this development in wavelet analysis is operator theory. This will be presented in the lectures, and we will also point to a number of developments in operator theory which in turn derive from wavelet problems, but which are of independent interest in mathematics. Some of the material will build on chapters in a new wavelet book, coauthored by the speaker and Ola Bratteli, see http://www.math.uiowa.edu/~jorgen/ .
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2004
 DOI:
 10.48550/arXiv.math/0403117
 arXiv:
 arXiv:math/0403117
 Bibcode:
 2004math......3117J
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Operator Algebras;
 42C40;
 46L60;
 47L30;
 42A16;
 43A65 (Primary);
 46L45;
 42A65;
 41A15 (Secondary)
 EPrint:
 63 pages, 10 figures/tables, LaTeX2e ("mrv9x6" document class), Contribution by Palle E. T. Jorgensen to the Tutorial Sessions, Program: ``Functional and harmonic analyses of wavelets and frames,'' 47 August 2004, Organizers: Judith Packer, Qiyu Sun, Wai Shing Tang. v2 adds Section 2.3.4, "Matrix completion" with references