  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, co-authored by the speaker and Ola Bratteli, see
http://www.math.uiowa.edu/~jorgen/ .
