turkmath.org

The classical Bernstein-Walsh theorem refers to the approximation of holomorphic functions by polynomials in the complex plane. In the multidimensional case, it was proved by J. Sichak (1962). The study of analytic functions on parabolic manifolds is currently an urgent problem and is the subject of research by many mathematicians (Stoll, Griffiths-King, Aytuna, Sadullaev, Zeriahi and others). This talk is devoted to the proof of analogue of the Bernstein-Walsh theorem on a parabolic manifold. The proof uses a new method, the embedding of a compact and parabolic manifold into a complex space of high dimension.