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

Dorin Ervin Dutkay·Kjetil Roysland
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Abstract

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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Dorin Ervin Dutkay, Kjetil Roysland. 2007-06-07. The algebra of harmonic functions for a matrix-valued transfer operator. https://arxiv.org/abs/math/0611539

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