TEST FUNCTIONS IN CONSTRAINED INTERPOLATION

被引：5

作者：

Dritschel, Michael A. ^{[1
]}

Pickering, James ^{[1
]}

机构：

[1] Newcastle Univ, Dept Math, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 364卷 / 11期

基金：

英国工程与自然科学研究理事会;

关键词：

Interpolation; realizations; Nevanlinna-Pick; test functions; NEVANLINNA-PICK INTERPOLATION;

D O I：

10.1090/S0002-9947-2012-05515-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a set of test functions for H-1(infinity), the algebra of bounded holomorphic functions on the disk with first derivative equal to 0; whose interpolation problem was studied by Davidson, Paulsen; Raghupathi and Singh (2009). We show that this set of test functions is minimal by relating these ideas to realization and interpolation problems.

引用

页码：5589 / 5604

页数：16

共 11 条

[1]

ABRAHAMSE MB, 1979, MICH MATH J, V26, P195

[2]

Agler J., 2002, GRADUATE STUDIES MAT

[3]

Agler Jim, 2008, MEMOIRS AM MATH SOC, V191, p[viii, 159]

[4] Reproducing kernels for Hardy spaces on multiply connected domains [J].

Ball, JA ;

Clancey, KF .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 1996, 25 (01) :35-57

[5]

Ball Joseph A., 2008, ARXIV08092345

[6] A Constrained Nevanlinna-Pick Interpolation Problem [J].

Davidson, Kenneth R. ;

Paulsen, Vern I. ;

Raghupathi, Mrinal ;

Singh, Dinesh .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2009, 58 (02) :709-732

[7] The failure of rational dilation on a triply connected domain [J].

Dritschel, MA ;

McCullough, S .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 18 (04) :873-918

[8]

McCullough S, 2002, INDIANA U MATH J, V51, P479

[9] Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains [J].

Pickering, James .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2010, 4 (01) :55-95

[10]

Raghupathi M, 2009, INTEGR EQUAT OPER TH, V63, P103, DOI 10.1007/s00020-008-1639-9

← 1 2 →