An Lp Analog to AAK Theory for p⩾2☆
An Lp Analog to AAK Theory for p⩾2☆
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DOI：
10.1006/jfan.2001.3860
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发表时间：
2002-05
影响因子：
1.7
通讯作者：
L. Baratchart;F. Seyfert
中科院分区：
文献类型：
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作者：
L. Baratchart;F. Seyfert
我们在单位圆上发展了一个类似于AAK理论的Lp，它在p=∞的情况（经典地求解最佳一致亚纯逼近）和p=2的情况（等价于H2-最佳有理逼近）之间连续插值.我们将结果应用于有理逼近的唯一性问题和具有两个分支点的函数的最佳亚纯逼近的极点的渐近行为。正如一位裁判所指出的，当Hankel算子的定义被适当地推广时，理论的一部分扩展到每个p∈[1，∞];我们结合V.A. Prokhorov，提交出版。
We develop an Lp analog to AAK theory on the unit circle that interpolates continuously between the case p=∞, which classically solves for best uniform meromorphic approximation, and the case p=2, which is equivalent to H2-best rational approximation. We apply the results to the uniqueness problem in rational approximation and to the asymptotic behaviour of poles of best meromorphic approximants to functions with two branch points. As pointed out by a referee, part of the theory extends to every p∈[1, ∞] when the definition of the Hankel operator is suitably generalized; this we discuss in connection with the recent manuscript by V. A. Prokhorov, submitted for publication.