Factorization of some triangular matrix functions and its applications

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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-29
Number of pages29
JournalOperators and Matrices
Volume9
Issue number1
DOIs
StatePublished - Jan 1 2015

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Triangular matrix
Matrix Function
Factorization
Fredholmness
Zero
Monomial
Real Line
Convolution
Union
Partial
Interval
Term
Form

Keywords

  • Almost periodic factorization
  • Convolution type equations
  • Fredholm operators
  • Geometric mean

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

Cite this

Factorization of some triangular matrix functions and its applications. / Karlovich, Yu I.; Loreto-Hernández, J.; Spitkovsky, Ilya.

In: Operators and Matrices, Vol. 9, No. 1, 01.01.2015, p. 1-29.

Research output: Contribution to journalArticle

Karlovich, Yu I. ; Loreto-Hernández, J. ; Spitkovsky, Ilya. / Factorization of some triangular matrix functions and its applications. In: Operators and Matrices. 2015 ; Vol. 9, No. 1. pp. 1-29.
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