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Two Problems on Coinvariant Subspaces of the Shift Operator

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Abstract

Two problems are posed that involve the star-invariant subspace \({K^{p}_{\theta}}\) (in the Hardy space H p) associated with an inner function \({\theta}\). One of these asks for a characterization of the extreme points of the unit ball in \({K^{\infty}_{\theta}}\), while the other concerns the Fermat equation f n + g n =  h n in \({K^{p}_{\theta}}\).

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References

  1. Garnett, J.B.: Bounded Analytic Functions, Revised first edition. Springer, New York (2007)

  2. de Leeuw K., Rudin W.: Extreme points and extremum problems in H 1. Pac. J. Math. 8, 467–485 (1958)

    Article  MATH  Google Scholar 

  3. Dyakonov K.M.: Extreme points in spaces of polynomials. Math. Res. Lett. 10, 717–728 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Konheim A.G., Rivlin T.J.: Extreme points of the unit ball in a space of real polynomials. Am. Math. Mon. 73, 505–507 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  5. Rack H.-J.: Extreme Punkte in der Einheitskugel des Vektorraumes der trigonometrischen Polynome. Elem. Math. 37, 164–165 (1982)

    MATH  MathSciNet  Google Scholar 

  6. Dyakonov K.M.: Interpolating functions of minimal norm, star-invariant subspaces, and kernels of Toeplitz operators. Proc. Am. Math. Soc. 116, 1007–1013 (1992)

    MATH  MathSciNet  Google Scholar 

  7. Dyakonov K.M.: Zeros of analytic functions, with or without multiplicities. Math. Ann. 352, 625–641 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gundersen G.G., Hayman W.K.: The strength of Cartan’s version of Nevanlinna theory. Bull. Lond. Math. Soc. 36, 433–454 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Sheil-Small, T.: Complex polynomials. Cambridge Studies in Advanced Mathematics, vol. 75. Cambridge University Press, Cambridge (2002)

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Authors and Affiliations

  1. Departament de Matemàtica Aplicada i Anàlisi, ICREA and Universitat de Barcelona, Gran Via, 585, 08007, Barcelona, Spain

    Konstantin M. Dyakonov

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  1. Konstantin M. Dyakonov
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Correspondence to Konstantin M. Dyakonov.

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Supported in part by grant MTM2011-27932-C02-01 from El Ministerio de Ciencia e Innovación (Spain) and grant 2009-SGR-1303 from AGAUR (Generalitat de Catalunya).

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Dyakonov, K.M. Two Problems on Coinvariant Subspaces of the Shift Operator. Integr. Equ. Oper. Theory 78, 151–154 (2014). https://doi.org/10.1007/s00020-013-2110-0

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  • DOI: https://doi.org/10.1007/s00020-013-2110-0

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