Harmonic Functions of a Transfer Operator
by
Beth P. Peterson
Lamar University

A prewavelet system can be associated with a Ruelle transfer operator and an h_\phi function derived from inner product of the prewavelet function that is both harmonic with respect the operator and nonconstant only when the prewavelet is a father function (Jorgensen, 1998). Using results of Conze and Raugi (1990), we show how to find, for prewavelets that are obtained by substitution, some techniques for finding h_\phi. We also find an algebraic method for obtaining the other generators of the transition operator's invariant space.

Date received: April 30, 1999