Maximal convergence theorems for functions of squared modulus holomorphic type in and some applications
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- 作者：Christiane Kraus
- 关键词：Polynomial approximation in 2-space ; Maximal convergence ; Bernstein– ; Walsh's type theorems ; Real-analytic functions
- 刊名：Journal of Approximation Theory
- 出版年：2007
- 出版时间：July 2007
- 年：2007
- 卷：147
- 期：1
- 页码：47-66
- 全文大小：315 K
文摘
In this paper we extend the theory of maximal convergence introduced by Walsh to functions of squared modulus holomorphic type, i.e.
where g is holomorphic in an open connected neighborhood of ![]()
. We introduce in accordance to the well-known complex maximal convergence number for holomorphic functions a real maximal convergence number for functions of squared modulus holomorphic type and prove several maximal convergence theorems. We achieve that the real maximal convergence number for F is always greater or equal than the complex maximal convergence number for g and equality occurs if L is a closed disk in ![]()
. Among other various applications of the resulting approximation estimates we show that for functions F of squared holomorphic type which have no zeros in ![]()
the relation