Almost Periodic Factorization of Some Triangular Matrix Functions

被引：10

作者：

Camara, M. C. ^{[1
]}

Karlovich, Yu. I. ^{[2
]}

Spitkovsky, I. M. ^{[3
]}

机构：

[1] Univ Tecn Lisboa, Inst Super Tecn, Dept Matemat, Lisbon, Portugal

[2] Univ Autonoma Estado Morelos, Fac Ciencia, Cuernavaca 62209, Morelos, Mexico

[3] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

来源：

MODERN ANALYSIS AND APPLICATIONS: MARK KREIN CENTENARY CONFERENCE, VOL 1: OPERATOR THEORY AND RELATED TOPICS | 2009年 / 190卷

关键词：

Almost periodic factorization; Toeplitz operator; RIEMANN-HILBERT PROBLEMS; CORONA THEOREM; CANONICAL FACTORIZATION; TOEPLITZ; SYMBOLS;

D O I：

10.1007/978-3-7643-9919-1_10

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper is devoted to matrices of the form G(x) = [(ei lambda x)(f(x)) (0)(e-i lambda x)], with almost periodic off-diagonal entry f. Some new cases are found, in terms of the Bohr-Fourier spectrum of f, in which G is factorable. Formulas for the partial indices are derived and, under additional constraints, the factorization itself is constructed explicitly. Some a priori conditions on the Bohr-Fourier spectra of the factorization factors (provided that a canonical factorization exists) are also given.

引用

页码：171 / +

页数：3

共 14 条

[1] Construction of sampling and interpolating sequences for multi-band signals. The two-band case [J].

Avdonin, Sergei ;

Bulanova, Anna ;

Moran, William .

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE, 2007, 17 (02) :143-156

[2] The corona theorem and the canonical factorization of triangular AP matrix functions - Effective criteria and explicit formulas [J].

Bastos, MA ;

Karlovich, YI ;

dos Santos, AF ;

Tishin, PM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 223 (02) :523-550

[3] The corona theorem and the existence of canonical factorization of triangular AP-matrix functions [J].

Bastos, MA ;

Karlovich, YI ;

dos Santos, AF ;

Tishin, PM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 223 (02) :494-522

[4] Oscillatory Riemann-Hilbert problems and the corona theorem [J].

Bastos, MA ;

Karlovich, YI ;

dos Santos, AF .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 197 (02) :347-397

[5]

Bottcher A., 2002, CONVOLUTION OPERATOR

[6] Invertibility of Toeplitz operators and corona conditions in a strip [J].

Camara, M. C. ;

Diogo, C. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 342 (02) :1297-1317

[7] A new approach to factorization of a class of almost-periodic triangular symbols and related Riemann-Hilbert problems [J].

Camara, M. C. ;

dos Santos, A. F. ;

Martins, M. C. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 235 (02) :559-592

[8] Wiener-Hopf factorization for a class of oscillatory symbols [J].

Câmara, MC ;

dos Santos, AF .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2000, 36 (04) :409-432

[9]

Corduneanu C., 1968, Almost Periodic Functions

[10]

KARLOVICH YI, 2005, APPROXIMATION APPROA, P143

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