Almost periodic factorization of 2 × 2 triangular matrix functions: New cases of off diagonal spectrum

Ashwin Rastogi, Leiba Rodman, Ilya M. Spitkovsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Many known results on almost periodic factorization of almost periodic 2 × 2 triangular matrix functions of the form (Formula presented.) are reviewed from a unified point of view, with particular attention to the case when the off diagonal entry is at most a quadrinomial almost periodic function. New results are obtained on almost periodic factorization for off diagonal entry having its Bohr-Fourier spectrum in a union of two shifted grids, i.e., arithmetic progressions, with the same difference, and perhaps an additional point. When specializing these results to the case of off diagonal almost periodic trinomials, new cases of factorability are obtained. The main technical tool is the Portuguese transformation, a known algorithm.

Original languageEnglish (US)
Title of host publicationTopics in Operator Theory
Subtitle of host publicationVolume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008
EditorsJoseph A. Ball, Vladimir Bolotnikov, Leiba Rodman, Ilya M. Spitkovsky, J. William Helton
PublisherSpringer International Publishing
Pages469-487
Number of pages19
ISBN (Print)9783034601573
DOIs
StatePublished - 2010
Event19th International Workshop on Operator Theory and its Applications, IWOTA 2008 - Williamsburg, United States
Duration: Jul 22 2008Jul 26 2008

Publication series

NameOperator Theory: Advances and Applications
Volume202
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Other

Other19th International Workshop on Operator Theory and its Applications, IWOTA 2008
CountryUnited States
CityWilliamsburg
Period7/22/087/26/08

Keywords

  • Almost periodic functions
  • Factorization
  • Portuguese transformation

ASJC Scopus subject areas

  • Analysis

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