A Local Expansion Theorem for the L?wner Equation

详细信息    查看全文

• 作者：Subhajit Ghosechowdhury
• 关键词：Reproducing Kernel Hilbert space ; Grunsky space ; Herglotz function ; Lö ; wner differential equation
• 刊名：Integral Equations and Operator Theory
• 出版年：2004
• 出版时间：January 2004
• 年：2004
• 卷：48
• 期：1
• 页码：1-25
• 全文大小：348 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989

文摘

If W(z) is a power series with complex coefficients which representsan injective function bounded by one in the unit disk and which vanishes atthe origin then a Grunsky space G(W)\mathcal{G}(W) exists. It is contained contractivelyin the Dirichlet space for the unit disk. In this paper an admissible family ofweighted Dirichlet spaces is used as in the proof of Bieberbach conjecture toconstruct a Local Grunsky space. An expansion theorem is presented for sucha Local Grunsky space. The proof relies on the reproducing kernel functionfor coefficients of powers of z and Löwner differential equation.