Carathéodory 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.
|Translated title of the contribution
|Carathéodory functions on a Riemann surface and associated reproducing kernel Hilbert spaces
|Number of pages
|Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
|Published - 1 Sep 2001
ASJC Scopus subject areas
- General Mathematics