The Nevanlinna-Pick interpolation problem in multiply connected domains

被引：0

作者：

Vinnikov V.L. ^{[1
]}

Fedorov S.I. ^{[2
]}

机构：

[1] Department of Theoretical mathematics, Weizmann Institute, Pexobot

[2] Department of Mathematics, University of Auckland, Auckland

来源：

Journal of Mathematical Sciences | 2001年 / 105卷 / 4期

关键词：

Hardy Space; Connect Domain; Positive Semidefinite; Interpolation Problem; Planar Domain;

D O I：

10.1023/A:1011368822699

中图分类号：

学科分类号：

摘要：

We simplify and strengthen Abrahamse's result on the Nevanlinna-Pick interpolation problem in a finitely connected planar domain, according to which the problem has a solution if and only if the Pick matrices associated with character-automorphic Hardy spaces are positive semidefinite for all characters in ℝn-1/ℤn-1, where n is the connectivity of the domain. The main aim of the paper is to reduce the indicated procedure (verification of the positive semidefiniteness) for the entire real (n-1)-torus ℝn-1/ℤn-1 to a part of it, whose dimension is, possibly, less than n-1. ©2001 Plenum Publishing Corporation.

引用

页码：2109 / 2126

页数：17

共 14 条

[1]

Goluzin G.M., Geometric Theory of Functions of a Complex Variable, (1969)

[2]

Nikol'Skii N.K., Treatise on the Shift Operator, (1986)

[3]

Fisher S.D., Function Theory on Planar Domains, (1983)

[4]

Sarason D., Generalized interpolation in H∞, Trans. Am. Math. Soc., 127, pp. 179-203, (1967)

[5]

Abrahamse M.B., The Pick interpolation theorem for finitely connected domains, Michigan Math. J., 26, pp. 195-203, (1979)

[6]

Fedorov S.I., Harmonic analysis in a multiply connected domain. I, II, Mat. Sb., 181, pp. 833-864, (1990)

[7]

Ball J.A., Clancey K.F., Reproducing kernels for Hardy spaces on multiply connected domains, Integral Equations Operator Theory, 25, pp. 35-57, (1996)

[8]

Fay J.D., Theta functions on Riemann surfaces, Lect. Notes Math., 352, (1973)

[9]

Clancey K.F., Representing measures on multiply connected domains, Illinois J. Math., 35, pp. 286-311, (1991)

[10]

Kra I., Automorphic Forms and Kleinian Groups, (1972)

← 1 2 →