Covariant representations for matrix-valued transfer operators

2007/01/16 by Dorin Ervin Dutkay, Dutkay, Dorin Ervin, Kjetil Røysland +1 · 1 citation
Mathematics · Computer Science · #Mathematical Analysis and Transform Methods #Image and Signal Denoising Methods #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0701453

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 ℝⁿ if the weight satisfies some low-pass condition.

Citations

• Subalgebras of C*-algebras

Cited by

• Dynamical properties of endomorphisms, multiresolutions, similarity-and orthogonality relations

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