Covariant representations for matrix-valued transfer operators

Dorin Ervin Dutkay; Kjetil Roysland

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Covariant representations for matrix-valued transfer operators

Dorin Ervin Dutkay·Kjetil Roysland

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Abstract

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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Dorin Ervin Dutkay, Kjetil Roysland. 2007-06-28. Covariant representations for matrix-valued transfer operators. https://arxiv.org/abs/math/0701453

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