Harmonic analysis of signed Ruelle transfer operators

AbstractMotivated by wavelet analysis, we prove that there is a one-to-one correspondence between the following data: (i)Solutions to R(h)=h where R is a certain non-positive Ruelle transfer operator;(ii)Operators that intertwine a certain class of representations of the C∗-algebra AN on two unitary generators U, V subject to the relation UVU−1=VN. 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