Strong asymptotic behavior and weak convergence of polynomials orthogonal on an arc of the unit circle

被引:4
|
作者
Hernández, MB
Díaz, EM
机构
[1] Univ La Rioja, Dept Matemat & Computac, Edificio JL Vives, Logrono 26004, Spain
[2] Inst Super Ciencias & Tecnol Nucl, Havana 10600, Cuba
关键词
D O I
10.1006/jath.2001.3574
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let sigma be a Finite positive Borel measure supported on an are gamma of the unit circle, such that sigma' > 0 a.e. on gamma. We obtain a theorem about the weal, convergence of the corresponding sequence of orthonormal polynomials. Moreover, we prove an analogue of the Szego-Geronimus theorem on strong asymptotics of the orthogonal polynomials on the complement of gamma, which completes to its full extent a result of N. 1. Akhiezer, The key tool in the proofs is the use of orthogonality with respect to varying measures. (C) 2001 Academic Press.
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页码:233 / 255
页数:23
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