Wavelets and Operator Relations
by
Palle Jorgensen
University of Iowa
Coauthors: O. Bratteli and D. Evans

The structure of orthogonal wavelets may be derived from a set of operator relations, one on L²(R) and one on the sequence space l². There is then an intertwining operation that relates the two, and makes a direct connection between wavelets and a class of representations of one of the Cuntz algebras, with O_n and n corresponding to the scaling number which defines the wavelet in question. An advantage of the wavelet approach is that it yields a basis free way of thinking about wavelets, and at the same time suggests new wavelet examples from representations of O_n, and of course, conversely, we get representations of O_n from known wavelets, representations that have independent significance, and which probably wouldn't have surfaced if it wasn't for the wavelet connection.

Date received: May 16, 1999