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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Dutkay, D.E., Røysland, K. Covariant Representations for Matrix-valued Transfer Operators. Integr. equ. oper. theory 62, 383–410 (2008). https://doi.org/10.1007/s00020-008-1623-4
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DOI: https://doi.org/10.1007/s00020-008-1623-4