Covariant representations for matrix-valued transfer operators

Details Covariant representations for matrix-valued transfer operators Covariant representations for matrix-valued transfer operators

2007-01-16

arxiv.org/abs/math/0701453v3

Mathematics

Functional Analysis

new version, motivation added

Scientific paper

Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence between the commutant of this structure and the fixed points of the transfer operator. We show how the covariant representation can be realized on $\mathbb{R}^n$ if the weight satisfies some low-pass condition.

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