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

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

2006-11-17

arxiv.org/abs/math/0611539v3

J. Funct. Anal. 252 (2007), no. 2, 734--762.

Mathematics

Functional Analysis

v2, corrected some typos

Scientific paper

We analyze matrix-valued transfer operators. We prove that the fixed points
of transfer operators form a finite dimensional $C^*$-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.

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