科研之友
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摘要
We consider the problem of finding the extremal function f which minimises the Bergman space A(2) norm for the class of non-vanishing functions whose first n+1 Taylor coefficients are given. We define an analytic function K in terms of f and show that the functions K and f satisfy a certain differential equation. This equation yields a set of relationships between the area moments and the circle moments of vertical bar f vertical bar(2), which in particular shows that the outer part of f is a polynomial of degree at most n.
- 出版日期2011-9
