SCALING BY 5 ON A 1/4-CANTOR MEASURE

摘要

Each Cantor measure mu with scaling factor 1/2n has at least one associated orthonormal basis of exponential functions (ONB) for L-2(mu). In the particular case where the scaling constant for the Cantor measure is 1/4 and two specific ONBs are selected for L-2(mu(1/4)), there is a unitary operator U defined by mapping one ONB to the other. This paper focuses on the case in which one ONB Gamma is the original Jorgensen-Pedersen ONB for the Cantor measure mu(1/4) and the other ONB is 5 Gamma. The main theorem of the paper states that the corresponding operator U is ergodic in the sense that only the constant functions are fixed by U.