Orthogonal polynomials and quadratic extremal problems
Orthogonal polynomials and quadratic extremal problems
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正交多项式和二次极值问题
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. McDougall
中科院分区：
文献类型：
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作者：
J. McDougall
本文分析了定义在各种解析函数Hilbert空间上的一类二次极值问题，从而推广了S. D.费希尔这里考虑的每个极值问题被证明是与一个系统的正交多项式。然后，正交多项式确定极值函数的性质，并提供关于极值存在的信息。
The purpose of this paper is to analyse a class of quadratic extremal problems defined on various Hilbert spaces of analytic functions, thereby generalizing an extremal problem on the Dirichlet space which was solved by S.D. Fisher. Each extremal problem considered here is shown to be connected with a system of orthogonal polynomials. The orthogonal polynomials then determine properties of the extremal function, and provide information about the existence of extremals.