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Harmonic Analysis of Signed Ruelle Transfer Operators

Dorin Ervin Dutkay
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Abstract

Motivated by wavelet analysis, we prove that there is a one-to-one correspondence between the following data: Solutions to $R(h)=h$ where $R$ is a certain non-positive Ruelle transfer operator; Operators that intertwine a certain class of representations of the $C^*$-algebra $\mathfrak{A}_N$ on two unitary generators $U$, $V$ subject to the relation $$UVU^{-1}=V^N$$ This correspondence enables us to give a criterion for the biorthogonality of a pair of scaling functions and calculate all solutions of the equation $R(h)=h$ in some concrete cases.

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Dorin Ervin Dutkay. 2002-02-11. Harmonic Analysis of Signed Ruelle Transfer Operators. https://arxiv.org/abs/math/0202097

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