Duality between eigenfunctions and eigendistributions of Ruelle and Koopman operators via an integral kernel

作者：Giulietti P^*; Lopes A O^*; Pit V^*

来源：Stochastics and Dynamics, 2016, 16(3): 1660011.

DOI：10.1142/S021949371660011X

• Transfer operator
• eigendistributions
• symbolic dynamics
• involution kernels

We consider the classical dynamics given by a one-sided shift on the Bernoulli space of d symbols. We study, on the space of Holder functions, the eigendistributions of the Ruelle operator with a given potential. Our main theorem shows that for any isolated eigenvalue, the eigendistributions of such Ruelle operator are dual to eigenvectors of a Ruelle operator with a conjugate potential. We also show that the eigenfunctions and eigendistributions of the Koopman operator satisfy a similar relationship. To show such results we employ an integral kernel technique, where the kernel used is the involution kernel.

• 出版日期2016-6