THE NON-TANGENTIAL BOUNDARY BEHAVIOR OF THE MATRIX-VALUED RATIONAL INNER FUNCTIONS ON BOUNDED SYMMETRIC DOMAIN

被引：0

作者：

Wang, Kai ^{[1
]}

Zhang, Shuyi ^{[2
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Fudan Univ, High Sch, Shanghai 200433, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年

基金：

中国国家自然科学基金;

关键词：

Rational inner function; bounded symmetric domain; non-tangential limit; QUOTIENT MODULES; THEOREM; INTEGRABILITY; SINGULARITIES; REGULARITY;

D O I：

10.1090/proc/16154

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Knese [Proc. LMS 111(2015), pp. 1261-1306] proved every rational inner function on polydisc has a non-tangential limit at every point of the Shilov boundary. We extended his result to the case of functions on general bounded symmetric domains. Namely, every rational inner function on a bounded symmetric domain has a non-tangential limit of modulus 1 at every point of the Shilov boundary. We also prove that every matrix-valued rational inner function on tube-type domain has a unitary non-tangential limit at every point of the Shilov boundary.

引用

页码：1539 / 1551

页数：13

共 43 条

[31] THE GENERALIZED BITANGENT CARATHEODORY-NEVANLINNA-PICK PROBLEM, AND [J, J(O)]-INNER MATRIX-VALUED FUNCTIONS
AROV, DZ
RUSSIAN ACADEMY OF SCIENCES IZVESTIYA MATHEMATICS, 1994, 42 (01): : 1 - 26
[32] GENERALIZED FACTORIZATION OF MATRIX-VALUED FUNCTIONS AND RIEMANN BOUNDARY-VALUE PROBLEM WITH INFINITE PARTIAL INDEXES
SPITKOVSKII, IM
DOKLADY AKADEMII NAUK SSSR, 1986, 286 (03): : 559 - 562
[33] SQUARE-INTEGRABILITY OF MATRIX-VALUED FUNCTIONS WITH RESPECT TO NON-NEGATIVE HERMITIAN MEASURE
ROSENBERG, M
DUKE MATHEMATICAL JOURNAL, 1964, 31 (02) : 291 - &
[34] SPECTRAL THEORY OF THE LINEAR-QUADRATIC OPTIMAL-CONTROL PROBLEM - ANALYTIC FACTORIZATION OF RATIONAL MATRIX-VALUED FUNCTIONS
JONCKHEERE, EA
SILVERMAN, LM
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1981, 19 (02) : 262 - 281
[35] ON A VECTORIAL RIEMANN BOUNDARY-VALUE PROBLEM WITH INFINITE DEFECT NUMBERS, AND RELATED FACTORIZATION OF MATRIX-VALUED FUNCTIONS
SPITOVSKII, IM
MATHEMATICS OF THE USSR-SBORNIK, 1988, 135 (3-4): : 521 - 538
[36] Spectral behavior of preconditioned non-Hermitian multilevel block Toeplitz matrices with matrix-valued symbol
Donatelli, Marco
Garoni, Carlo
Mazza, Mariarosa
Serra-Capizzano, Stefano
Sesana, Debora
APPLIED MATHEMATICS AND COMPUTATION, 2014, 245 : 158 - 173
[37] A multiple point Nevanlinna-Pick type interpolation problem with both interior and boundary data for Caratheodory matrix-valued functions
Hu Yong-Jian
Song Yan-Ping
Chen Gong-Ning
MATHEMATISCHE NACHRICHTEN, 2011, 284 (10) : 1304 - 1328
[38] SHARP ESTIMATES OF DEFECT NUMBERS OF A GENERALIZED RIEMANN BOUNDARY-VALUE PROBLEM, FACTORIZATION OF HERMITIAN MATRIX-VALUED FUNCTIONS AND SOME PROBLEMS OF APPROXIMATION BY MEROMORPHIC FUNCTIONS
LITVINCHUK, GS
SPITKOVSKII, IM
MATHEMATICS OF THE USSR-SBORNIK, 1982, 117 (02): : 205 - 224
[39] The Non–symmetric Discrete Algebraic Riccati Equation and Canonical Factorization of Rational Matrix Functions on the Unit Circle
A. E. Frazho
M. A. Kaashoek
A. C. M. Ran
Integral Equations and Operator Theory, 2010, 66 : 215 - 229
[40] The Non-symmetric Discrete Algebraic Riccati Equation and Canonical Factorization of Rational Matrix Functions on the Unit Circle
Frazho, A. E.
Kaashoek, M. A.
Ran, A. C. M.
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2010, 66 (02) : 215 - 229

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