Nonexistence of spectral gaps in Hölder spaces for continuous time dynamical systems

Abstract

We show that there is a natural restriction on the smoothness of spaces where the transfer operator for a continuous dynamical system has a spectral gap. Such a space cannot be embedded in a Hölder space with Hölder exponent greater than 1/2 unless it consists entirely of coboundaries.

This is part of the original version of arXiv:2102.00026 and is to appear in Israel J. Math