Abstract:

In my talk, I discuss general endomorphisms of a probability standard measure, their properties, and linear operators related to endomorphisms. The cases of measure preserving and nonsingular endomorphisms are considered. The set of generalized wavelet filters is explicitly described. Generators of Cuntz algebra representations are constructed in terms of wavelet filters and composition operators for any endomorphism. 

The talk is based on a joint paper with Palle Jorgensen.