TY - GEN

T1 - Almost periodic factorization of 2 × 2 triangular matrix functions

T2 - 19th International Workshop on Operator Theory and its Applications, IWOTA 2008

AU - Rastogi, Ashwin

AU - Rodman, Leiba

AU - Spitkovsky, Ilya M.

N1 - Funding Information:
The research leading to this paper was done while the first author was an undergraduate at the College of William and Mary. All authors were partially supported by NSF grant DMS-0456625.
Publisher Copyright:
© 2010 Birkhäuser Verlag Basel/Switzerland.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Almost periodic functions

KW - Factorization

KW - Portuguese transformation

UR - http://www.scopus.com/inward/record.url?scp=84975687646&partnerID=8YFLogxK

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U2 - 10.1007/978-3-0346-0158-0_26

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

M3 - Conference contribution

AN - SCOPUS:84975687646

SN - 9783034601573

T3 - Operator Theory: Advances and Applications

SP - 469

EP - 487

BT - Topics in Operator Theory

A2 - Ball, Joseph A.

A2 - Bolotnikov, Vladimir

A2 - Rodman, Leiba

A2 - Spitkovsky, Ilya M.

A2 - Helton, J. William

PB - Springer International Publishing

Y2 - 22 July 2008 through 26 July 2008

ER -