Caratheodory functions on a Riemann surface and associated reproducing kernel Hilbert spaces

Caratheodory functions are functions which are analytic and with a positive real part in the open upper half-plane C+. They are associated to reproducing kernel Hilbert spaces (with reproducing kernel of the form (2)) and play an important role in moment problems and in prediction theory of second order stationary processes. We study their counterpart in the setting of compact real Riemann surfaces. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.