Constructive almost periodic factorization of some triangular matrix functions

M. C. Câmara, Yu I. Karlovich, I. M. Spitkovsky

Research output: Contribution to journalArticle

Abstract

A factorability criterion is obtained constructively, and the respective factorization obtained explicitly, for 2 × 2 triangular almost periodic matrix functions of the form [(eλ, 0; f, e- λ)]. Here f = c- 1 e- α - c0 + c1 eβ, eμ (x) : = ei μ x, cj are non-zero constants and 0 < α, β, α + β < λ ≤ α + β + max {α, β} with α / β being irrational. Note that the factorization problem, even for triangular matrix functions as above with an arbitrary trinomial f, is open. The result obtained is yet another step towards its solution.

Original languageEnglish (US)
Pages (from-to)416-433
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume367
Issue number2
DOIs
StatePublished - Jul 15 2010

Keywords

  • Almost periodic factorization

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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