- Title: On the q-Bremermann-Dirichlet problem and polynomial convexity for unbounded sets - Speaker: Dr. Thomas Pawlaschyk (Universität Wuppertal)- Abstract: Part 1: Let D be an unbounded domain in C^n and let f be a bounded continuous function on the boundary bD of D. I show that under some (strong) conditions on D we can find a unique continuous extension F of f into D which is q-plurisubharmonic, (n-q-1)-plurisuperharmonic and which is maximal in the following sense: each q-plurisubharmonic function g on D with g <= f on bD satisfies g <= F on D. Part 2: I present recent results on polynomial convexity for unbounded closed sets and the relation to approximation of holomorphic functions defined on polynomially convex sets by entire ones. - Place: GAIA Seminar Room (# 106, Math Science bldg.) |

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