Factorization of some triangular matrix functions and its applications

Yu I. Karlovich; J. Loreto-Hernández; I. M. Spitkovsky

doi:10.7153/oam-09-01

Factorization of some triangular matrix functions and its applications

Yu I. Karlovich, J. Loreto-Hernández, I. M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider defined on the real line ℝ matrix functions with monomial terms of the form ce^iλx on the main diagonal and one row, and with zero entries elsewhere. The factorability of such matrices is established and, moreover, the algorithm for their factorization is provided. In particular, formulas for the partial indices are derived, and conditions for them to all equal zero (that is, for the factorization to be canonical) are stated. These results are then used to obtain Fredholmness criteria for some convolution type equations on unions of intervals.

Original language	English (US)
Pages (from-to)	1-29
Number of pages	29
Journal	Operators and Matrices
Volume	9
Issue number	1
DOIs	https://doi.org/10.7153/oam-09-01
State	Published - Mar 1 2015

Keywords

Almost periodic factorization
Convolution type equations
Fredholm operators
Geometric mean

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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N2 - We consider defined on the real line ℝ matrix functions with monomial terms of the form ceiλx on the main diagonal and one row, and with zero entries elsewhere. The factorability of such matrices is established and, moreover, the algorithm for their factorization is provided. In particular, formulas for the partial indices are derived, and conditions for them to all equal zero (that is, for the factorization to be canonical) are stated. These results are then used to obtain Fredholmness criteria for some convolution type equations on unions of intervals.

AB - We consider defined on the real line ℝ matrix functions with monomial terms of the form ceiλx on the main diagonal and one row, and with zero entries elsewhere. The factorability of such matrices is established and, moreover, the algorithm for their factorization is provided. In particular, formulas for the partial indices are derived, and conditions for them to all equal zero (that is, for the factorization to be canonical) are stated. These results are then used to obtain Fredholmness criteria for some convolution type equations on unions of intervals.

KW - Almost periodic factorization

KW - Convolution type equations

KW - Fredholm operators

KW - Geometric mean

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Factorization of some triangular matrix functions and its applications

Abstract

Keywords

ASJC Scopus subject areas

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