Strict transfer operator approaches for non-compact hyperbolic orbisurfaces

TL;DR

This paper develops strict transfer operator methods for a broad class of hyperbolic orbisurfaces, linking their Fredholm determinants to Selberg zeta functions, thus advancing spectral analysis techniques.

Contribution

It introduces explicit transfer operator families for hyperbolic orbisurfaces without cusps, extending previous methods to infinite-area cases and unifying approaches for all such orbifolds.

Findings

Constructed explicit transfer operators for non-compact hyperbolic orbisurfaces

Established the equivalence of Fredholm determinants and Selberg zeta functions

Extended transfer operator techniques to infinite-area hyperbolic orbifolds

Abstract

By building on former results and the cusp expansion algorithm, we construct strict transfer operator approaches for geometrically finite developable hyperbolic orbisurfaces of infinite area without cusps. Together with the cusp expansion algorithm for orbisurfaces with cusps, this provides strict transfer operator approaches for all hyperbolic orbifolds fulfilling mild assumptions. For every such orbisurface we obtain explicit transfer operator families for which, by virtue of a result of Fedosova and Pohl, the Fredholm determinant function is seen to be identical to the associated Selberg zeta function.