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Applications of Blaschke Products to the Spectral Theory of Toeplitz Operators

  • Sergei Grudsky
  • Eugene ShargorodskyEmail author
Chapter
Part of the Fields Institute Communications book series (FIC, volume 65)

Abstract

The chapter is a survey of some applications of Blaschke products to the spectral theory of Toeplitz operators. Topics discussed include Toeplitz operators with bounded measurable symbols, factorisation with an infinite index, compositions with Blaschke products, representation of functions with a given asymptotic behaviour of the argument in a neighbourhood of a discontinuity in the form of a composition of a continuous function with a Blaschke product, and applications to the KdV equation.

Keywords

Toeplitz operators Spectral theory Discontinuous symbols Blaschke products 

Mathematics Subject Classification

47B35 30J10 47A10 30H10 

Notes

Acknowledgements

The first author was supported by PROMEP (México) via “Proyecto de Redes” and by CONACYT grant 102800.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Departamento de MatematicasCINVESTAV del I.P.N.Mexico, D.F.Mexico
  2. 2.Department of MathematicsKing’s College LondonLondonUK

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