The algebra of harmonic functions for a matrix-valued transfer operator

Abstract

We analyze matrix-valued transfer operators. We prove that the fixed points of transfer operators form a finite dimensional $C^{\ast }$-algebra. For matrix weights satisfying a low-pass condition we identify the minimal projections in this algebra as correlations of scaling functions, i.e., limits of cascade algortihms.

v2, corrected some typos

References in corpus (1)

• Transfer operators for ${\Gamma }_0(n)$ and the Hecke operators for the period functions for $PSL(2,Z)$

Cited by in corpus (1)

• Projective multi-resolution analyses arising from direct limits of Hilbert modules