Bernstein Type Inequalities for Restrictions of Polynomials to Complex Submanifolds of ${\mathbb{C}}^{\mathbf{N}}$

Abstract

The paper studies Bernstein type inequalities for restrictions of holomorphic polynomials to graphs ${\Gamma }_f\subset {\mathbb{C}}^{n+m}$ of holomorphic maps $f:{\mathbb{C}}^n\to {\mathbb{C}}^m$. We establish general properties of exponents in such inequalities and describe some classes of graphs admitting Bernstein type inequalities of optimal exponents and of exponents of polynomial growth.

44 pages

References in corpus (1)

• On Local Behavior of Holomorphic Functions Along Complex Submanifolds of C^N