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The Operator Fejér-Riesz Theorem

  • Michael A. Dritschel
  • James Rovnyak
Part of the Operator Theory Advances and Applications book series (OT, volume 207)

Abstract

The Fejér-Riesz theorem has inspired numerous generalizations in one and several variables, and for matrix- and operator-valued functions. This paper is a survey of some old and recent topics that center around Rosenblum’s operator generalization of the classical Fejér-Riesz theorem.

Mathematics Subject Classification (2000)

Primary 47A68 Secondary 60G25 47A56 47B35 42A05 32A70 30E99 

Keywords

Trigonometric polynomial Fejér-Riesz theorem spectral factorization Schur complement noncommutative polynomial Toeplitz operator shift operator 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Michael A. Dritschel
    • 1
  • James Rovnyak
    • 2
  1. 1.School of Mathematics and Statistics Herschel BuildingUniversity of NewcastleNewcastle upon TyneUK
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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