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

Ashwin Rastogi; Leiba Rodman; Ilya M. Spitkovsky

doi:10.1007/978-3-0346-0158-0_26

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

Ashwin Rastogi, Leiba Rodman, Ilya M. Spitkovsky

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Topics in Operator Theory
Subtitle of host publication	Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008
Editors	Joseph A. Ball, Vladimir Bolotnikov, Leiba Rodman, Ilya M. Spitkovsky, J. William Helton
Publisher	Springer International Publishing
Pages	469-487
Number of pages	19
ISBN (Print)	9783034601573
DOIs	https://doi.org/10.1007/978-3-0346-0158-0_26
State	Published - 2010
Event	19th International Workshop on Operator Theory and its Applications, IWOTA 2008 - Williamsburg, United States Duration: Jul 22 2008 → Jul 26 2008

Publication series

Name	Operator Theory: Advances and Applications
Volume	202
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Other

Other	19th International Workshop on Operator Theory and its Applications, IWOTA 2008
Country/Territory	United States
City	Williamsburg
Period	7/22/08 → 7/26/08

Keywords

Almost periodic functions
Factorization
Portuguese transformation

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/978-3-0346-0158-0_26

Cite this

Rastogi, A., Rodman, L., & Spitkovsky, I. M. (2010). Almost periodic factorization of 2 × 2 triangular matrix functions: New cases of off diagonal spectrum. In J. A. Ball, V. Bolotnikov, L. Rodman, I. M. Spitkovsky, & J. W. Helton (Eds.), Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008 (pp. 469-487). (Operator Theory: Advances and Applications; Vol. 202). Springer International Publishing. https://doi.org/10.1007/978-3-0346-0158-0_26

Almost periodic factorization of 2 × 2 triangular matrix functions: New cases of off diagonal spectrum. / Rastogi, Ashwin; Rodman, Leiba; Spitkovsky, Ilya M.
Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008. ed. / Joseph A. Ball; Vladimir Bolotnikov; Leiba Rodman; Ilya M. Spitkovsky; J. William Helton. Springer International Publishing, 2010. p. 469-487 (Operator Theory: Advances and Applications; Vol. 202).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Rastogi, A, Rodman, L & Spitkovsky, IM 2010, Almost periodic factorization of 2 × 2 triangular matrix functions: New cases of off diagonal spectrum. in JA Ball, V Bolotnikov, L Rodman, IM Spitkovsky & JW Helton (eds), Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008. Operator Theory: Advances and Applications, vol. 202, Springer International Publishing, pp. 469-487, 19th International Workshop on Operator Theory and its Applications, IWOTA 2008, Williamsburg, United States, 7/22/08. https://doi.org/10.1007/978-3-0346-0158-0_26

Rastogi A, Rodman L, Spitkovsky IM. Almost periodic factorization of 2 × 2 triangular matrix functions: New cases of off diagonal spectrum. In Ball JA, Bolotnikov V, Rodman L, Spitkovsky IM, Helton JW, editors, Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008. Springer International Publishing. 2010. p. 469-487. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-0346-0158-0_26

Rastogi, Ashwin ; Rodman, Leiba ; Spitkovsky, Ilya M. / Almost periodic factorization of 2 × 2 triangular matrix functions : New cases of off diagonal spectrum. Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008. editor / Joseph A. Ball ; Vladimir Bolotnikov ; Leiba Rodman ; Ilya M. Spitkovsky ; J. William Helton. Springer International Publishing, 2010. pp. 469-487 (Operator Theory: Advances and Applications).

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

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