Sur les fonctions analytiques f(x,y) dont l'ensemble des zéros par rapport a y est algébrique
The algebraically closed field of Nash functions is introduced. It is shown that this field is an algebraic closure of the field of rational functions in several variables. We give conditions for the irreducibility of polynomials with Nash coefficients, a description of factors of a polynomial over the field of Nash functions and a theorem on continuity of factors.
We show that the projections of the pluripolar hull of the graph of an analytic function in a subdomain of the complex plane are open in the fine topology.
Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.
General versions of Glicksberg's theorem concerning zeros of holomorphic maps and of Hurwitz's theorem on sequences of analytic functions is extended to infinite dimensional Banach spaces.