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Collectanea mathematica

, Volume 62, Issue 1, pp 27–55 | Cite as

Majorization in de Branges spaces II. Banach spaces generated by majorants

  • Anton Baranov
  • Harald Woracek
Article
  • 40 Downloads

Abstract

This is the second part in a series dealing with subspaces of de Branges spaces of entire functions generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banach spaces generated by admissible majorants. We study their interplay with the original de Branges space structure, and their geometry. In particular, we will show that, generically, they will be nonreflexive and nonseparable.

Keywords

de Branges subspace Majorant Banach space 

Mathematics Subject Classification (2000)

46E15 46B26 46E22 

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References

  1. 1.
    Ahern P.R., Clark D.N.: Radial limits and invariant subspaces. Amer. J. Math. 92(2), 332–342 (1970)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Baranov A.D.: Isometric embeddings of the spaces K θ in the upper half-plane. J. Math. Sci. 105(5), 2319–2329 (2001)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Baranov A.: Polynomials in the de Branges spaces of entire functions. Ark. Mat. 44(1), 16–38 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Baranov A.D., Havin V.P.: Admissible majorants for model subspaces and arguments of inner functions. Funct. Anal. Appl. 40(4), 249–263 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Baranov A., Woracek H.: Subspaces of de Branges spaces generated by majorants. Can. Math. J. 61(3), 503–517 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Baranov A., Woracek H.: Finite dimensional de Branges subspaces generated by majorants. Oper. Theory Adv. Appl. 188, 45–56 (2008)Google Scholar
  7. 7.
    Baranov A., Woracek H.: Majorization in de Branges spaces I. Representability of subspaces. J. Funct. Anal. 258(8), 2601–2636 (2010)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Borichev, A., Sodin, M.: Weighted polynomial approximation and the Hamburger moment problem. In: Complex analysis and differential equations, Proceedings of the Marcus Wallenberg Symposium in Honor of Matts Essén, Uppsala University (1998)Google Scholar
  9. 9.
    Bourbaki N.: General Topology. Hermann, Paris (1966)Google Scholar
  10. 10.
    de Branges L.: Some Hilbert spaces of entire functions. Proc. Amer. Math. Soc. 10(5), 840–846 (1959)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    de Branges L.: Hilbert Spaces of Entire Functions. Prentice-Hall, London (1968)zbMATHGoogle Scholar
  12. 12.
    Dym H., McKean H.: Gaussian Processes, Function Theory, and the Inverse Spectral Problem. Academic Press, New York (1976)zbMATHGoogle Scholar
  13. 13.
    Garnett J.B.: Bounded Analytic Functions. Academic Press, New York (1981)zbMATHGoogle Scholar
  14. 14.
    Gohberg, I., Krein, M.G.: Introduction to the theory of linear nonselfadjoint operators, Izdat. Nauka, Moscow, 1965 (in Russian). English translation: Translations of Mathematical Monographs 18, American Mathematical Society, Rhode Island (1969)Google Scholar
  15. 15.
    Gohberg, I., Kreĭn, M.G.: Theory and applications of Volterra operators in Hilbert space. Translations of Mathematical Monographs, AMS. Providence, Rhode Island (1970)Google Scholar
  16. 16.
    Hassi S., de Snoo H.S.V., Winkler H.: Boundary-value problems for two-dimensional canonical systems. Integr. Equ. Oper. Theory 36(4), 445–479 (2000)zbMATHCrossRefGoogle Scholar
  17. 17.
    Havin V.P., Mashreghi J.: Admissible majorants for model subspaces of H 2. Part I: slow winding of the generating inner function. Can. J. Math. 55(6), 1231–1263 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Kaltenbäck M., Woracek H.: De Branges spaces of exponential type: general theory of growth. Acta Sci. Math (Szeged) 71(1/2), 231–284 (2005)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Megginson R.: An Introduction to Banach space theory, GTM 183. Springer, New York (1998)Google Scholar
  20. 20.
    Rosenblum M., Rovnyak J.: Topics in Hardy Classes and Univalent Functions. Birkhäuser, Basel (1994)zbMATHGoogle Scholar

Copyright information

© Universitat de Barcelona 2010

Authors and Affiliations

  1. 1.Department of Mathematics and MechanicsSaint Petersburg State UniversityPetrodvoretsRussia
  2. 2.Institut für Analysis und Scientific ComputingTechnische Universität WienWienAustria

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