Dual mixing and quasi-mixing of inner function restrictions

Abstract

Dual quasi-mixing and dual mixing of a measure preserving transformation are uniform individual ratio limit properties of the transfer operator which entail the quasi-mixing and mixing properties of Krickeberg (respectively). The real restriction of a normalised, parabolic inner function of the upper half plane preserves Lebesgue measure and is dual mixing iff it is exact. Certain other restrictions are ``singular'' dual quasi-mixing.