Acta Mathematica

, Volume 177, Issue 2, pp 275–310

Beurling's Theorem for the Bergman space

  • A. Aleman
  • S. Richter
  • C. Sundberg


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  1. [ABFP]Apostol, C., Bercovici, H., Foias, C. &Pearcy, C., Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra.J. Funct. Anal., 63 (1985), 369–404.CrossRefMathSciNetGoogle Scholar
  2. [AR]Aleman, A. &Richter, S., Simply invariant subspaces ofH 2 of some multiply connected regions.Integral Equations Operator Theory, 24 (1996), 127–155.CrossRefMathSciNetGoogle Scholar
  3. [B]Beurling, A., On two problems concerning linear transformations in Hilbert space.Acta Math., 81 (1949), 239–255.MATHGoogle Scholar
  4. [BH]Borichev, A. & Hedenmalm, H., Harmonic functions of maximal growth: invertibility and cyclicity in Bergman spaces. Preprint.Google Scholar
  5. [D]Duren, P. L.,Theory of H p-Spaces. Academic Press, New York-London, 1970.Google Scholar
  6. [DKSS1]Duren, P. L., Khavinson, D., Shapiro, H. S. &Sundberg, O., Contractive zerodivisors in Bergman spaces.Pacific. J. Math. 157 (1993), 37–56.MathSciNetGoogle Scholar
  7. [DKSS2]—, Invariant subspaces in Bergman spaces and the biharmonic equation.Michigan Math. J., 41 (1994), 247–259.CrossRefMathSciNetGoogle Scholar
  8. [Gara]Garabedian, P. R.,Partial Differential Equations, John Wiley & Sons, New York-London-Sydney, 1964.Google Scholar
  9. [Garn]Garnett, J. B.,Bounded Analytic Functions, Academic Press, New York-London, 1981.Google Scholar
  10. [Hal]Halmos, P. R., Shifts on Hilbert spaces.J. Reine Angew. Math., 208 (1961), 102–112.MATHMathSciNetGoogle Scholar
  11. [Hed1]Hedenmalm, H., A factorization theorem for square area-integrable functions.J. Reine Angew. Math., 422 (1991), 45–68.MATHMathSciNetGoogle Scholar
  12. [Hed2]—, A factoring theorem for the Bergman space.Bull. London Math. Soc., 26 (1994), 113–126.MATHMathSciNetGoogle Scholar
  13. [Her]Herrero, D., On multicyclic operators.Integral Equations Operator Theory, 1 (1978), 57–102.CrossRefMATHMathSciNetGoogle Scholar
  14. [HKZ]Hedenmalm, H., Korenblum, B. &Zhu, K., Beurling type invariant subspaces of the Bergman space.J. London Math. Soc (2), 53 (1996), 601-614.MathSciNetGoogle Scholar
  15. [HRS]Hedenmalm, H., Richter, S. &Seip, K., Interpolating sequences and invariant subspaces of given index in the Bergman spaces.J. Reine Angew. Math, 477 (1996), 13–30.MathSciNetGoogle Scholar
  16. [Koo]Koosis, P.,Introduction to H p Spaces. Cambridge Univ. Press, New York, 1980.Google Scholar
  17. [Kor]Korenblum, B., Outer functions and cyclic elements in Bergman spaces.J. Funct. Anal., 115 (1993), 104–118.CrossRefMATHMathSciNetGoogle Scholar
  18. [KS]Khavinson, D. &Shapiro, H. S., Invariant subspaces in Bergman spaces and Hedenmalm's boundary value problem.Ark. Mat., 32 (1994), 309–321.MathSciNetGoogle Scholar
  19. [M]Mirsky, L.,An Introduction to Linear Algebra. Oxford Univ. Press, 1963.Google Scholar
  20. [R]Richter, S., Invariant subspaces of the Dirichlet shift.J. Reine Angew. Math., 386 (1988), 205–220.MATHMathSciNetGoogle Scholar
  21. [S1]Shapiro, H. S., Weighted polynomial approximation and boundary behaviour of analytic functions, inContemporary Problems in Analytic Functions (Erevan, 1965). Nauka, Moscow, 1966.Google Scholar
  22. [S2]—, Some remarks on weighted polynomial approximation of holomorphic functions.Mat. Sb., 73 (1967), 320–330; English translation in Math.USSR-Sb., 2 (1967), 285–294.MATHMathSciNetGoogle Scholar

Copyright information

© Institut Mittag-Leffler 1996

Authors and Affiliations

  • A. Aleman
    • 1
  • S. Richter
    • 2
  • C. Sundberg
    • 2
  1. 1.Fachbereich MathematikFernuniversität HagenHagenGermany
  2. 2.Department of MathematicsUniversity of TennesseeKnoxvilleU.S.A.

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