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Almost Periodic Factorization of 2 × 2 Triangular Matrix Functions: New Cases of Off Diagonal Spectrum

  • Ashwin Rastogi
  • Leiba Rodman
  • Ilya M. Spitkovsky
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)

Abstract

Many known results on almost periodic factorization of almost periodic 2 × 2 triangular matrix functions of the form \( \left[ {\begin{array}{*{20}c} {e^{i\lambda x} } & 0 \\ * & {e^{ - i\lambda x} } \\ \end{array} } \right] \) 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.

Keywords

Almost periodic functions factorization Portuguese transformation 

Mathematics Subject Classification (2000)

Primary 47A68 Secondary 42A75 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Ashwin Rastogi
    • 1
  • Leiba Rodman
    • 2
  • Ilya M. Spitkovsky
    • 2
  1. 1.Department of PhysicsHarvard UniversityCambridgeUSA
  2. 2.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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