A CLASS OF COMPOUND VECTOR-VALUED PROBLEM AND FACTORIZATION OF MATRIX FUNCTION

doi:10.1016/S0252-9602(10)60034-3

Abstract

Abstract:

In this article, we consider a class of compound vector-valued problem on upper-half plane C₊, which consists of vector Riemann problem along a closed contour in C₊ with matrix coefficient in Hölder class and vector Hilbert problem on the real axis with essential bounded measurable matrix coefficient. Under appropriate assumption we obtain its solution by use of Corona theorem and factorization of matrix functions in decomposed Banach algebras.

Key words: compound vector-valued problem, Corona theorem, canonical factorization, Hardy space

CLC Number:

42C05

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GUO Guo-An, DU Jin-Yuan. A CLASS OF COMPOUND VECTOR-VALUED PROBLEM AND FACTORIZATION OF MATRIX FUNCTION[J].Acta mathematica scientia,Series B, 2010, 30(1): 173-179.

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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(10)60034-3

http://121.43.60.238/sxwlxbB/EN/Y2010/V30/I1/173

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References

[1] Gohberg I, Kaashoek M A, Spitkovsky I M. An overview of matrix factorization theory and operator applications.
Operator Theory: Advances and Applications, 2003, 141: 1--102

[2] Litvinchuk G S, Spitkovskii I M. Factorization of Measurable Matrix Functions. Basel: Birkhäuser Verlag, 1987

[3] Bastos M A, Karlovich Yu I, Santos A F. Oscillatory Riemann-Hilbert problems and the Corona theorem. J Funct Analysis, 2003, 197: 347--397

[4] Clancy K, Gohberg I. Factorization of Matrix Functions and Singular Integral Operators. Boston: Birkhäuser Verlag, 1981

[5] Câmara M C, Malheiro M T. Wiener-Hopf factorization for a group of exponentials of nilpotent matrices. Linear Algebra Appl, 2000, 320: 79--96

[6] Du Zhihua. A simi-conjugate matrix boundary value problem for general orthogonal polynomials on an arbitrary smooth jordan curve. Acta Mathematica Scientia, 2008, 28B(2): 401--407

[7] Mikhlin S G, Pr\"{o}ssdorf S. Singular Integral Operators. Berlin: Springer-Verlag, 1986

[8] Garnett J B. Bounded Analytic Functions. New York: Academic Press, 1981

[9] Lu Jianke. Boundary Value Problems for Analytic Functions. Singapore: World Scientific, 1993

[10] Lu Jianke. On compoud boundary problems. Scientia Sinica, 1965, 141: 1545--1555

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