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||The 17 Hilbert problem for global analytic functions on dimension n
||Prof. Jose Fernando Galvan |
(Univ. Complutense, Madrid)
|orario delle lezioni|
The 17th Hilbert's problem consists of representing semidefinite positive functions as sums of squares.
An answer to this problem is known for several rings of functions: nevertheless in the case of global analytic function this problem is still open.
In these lectures we present several advances in the direction of reducing the problem to an "irreducible" case.
In fact this reduction actually provides further informations concerning the quantitative aspects of the problem, for instance, about finiteness of the Pythagoras number of the field of meromorphic functions on R^n.
Prerequisiti: Nozioni base di Analisi Complessa di piu' variabili
(Lezioni in italiano)