Mitja Nedić: The convex combination problem for Herglotz-Nevanlinna functions
Title: The convex combination problem for Herglotz-Nevanlinna functions.
Abstract: Herglotz-Nevanlinna functions are holomorphic functions defined in the poly-upper half-plane having non-negative imaginary part. Any such function admits an integral representation formula involving a real number, a vector of non-negative numbers and a positive Borel measure on R^n satisfying certain properties. These parameters are of great interest as they completely characterize this class of functions. The convex combination problem for Herglotz-Nevanlinna functions asks whether we can relate the parameters of a Herglotz-Nevanlinna function in one variable to the parameters of a Herglotz-Nevanlinna function in several variables, if the several-variable function was built out of the one-variable function by replacing the independent variable with a convex combination of independent variables. In this talk, we present a completely explicit solution to this problem.
Seminar bo v PLEMLJEVEM SEMINARJU na Jadranski 19. Vljudno vabljeni!
Vodji seminarja
Josip Globevnik in Franc Forstnerič
