Acta Mathematica

Beurling's Theorem for the Bergman space

A. Aleman, S. Richter, and C. Sundberg

Full-text: Open access

Note

A part of this work was done while the second author was visiting the University of Hagen. The second and third authors were supported in part by the National Science Foundation.

Article information

Source
Acta Math. Volume 177, Number 2 (1996), 275-310.

Dates
Received: 15 May 1995
First available in Project Euclid: 31 January 2017

Permanent link to this document
http://projecteuclid.org/euclid.acta/1485890984

Digital Object Identifier
doi:10.1007/BF02392623

Zentralblatt MATH identifier
0886.30026

Rights
1996 © Institut Mittag-Leffler

Citation

Aleman, A.; Richter, S.; Sundberg, C. Beurling's Theorem for the Bergman space. Acta Math. 177 (1996), no. 2, 275--310. doi:10.1007/BF02392623. http://projecteuclid.org/euclid.acta/1485890984.


Export citation

References

  • [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.
  • [AR] Aleman, A. & Richter, S., Simply invariant subspaces of H2 of some multiply connected regions. Integral Equations Operator Theory, 24 (1996), 127–155.
  • [B] Beurling, A., On two problems concerning linear transformations in Hilbert space. Acta Math., 81 (1949), 239–255.
  • [BH] Borichev, A. & Hedenmalm, H., Harmonic functions of maximal growth: invertibility and cyclicity in Bergman spaces. Preprint.
  • [D] Duren, P. L., Theory of Hp-Spaces. Academic Press, New York-London, 1970.
  • [DKSS1] Duren, P. L., Khavinson, D., Shapiro, H. S. & Sundberg, O., Contractive zerodivisors in Bergman spaces. Pacific. J. Math. 157 (1993), 37–56.
  • [DKSS2]—, Invariant subspaces in Bergman spaces and the biharmonic equation. Michigan Math. J., 41 (1994), 247–259.
  • [Gara] Garabedian, P. R., Partial Differential Equations, John Wiley & Sons, New York-London-Sydney, 1964.
  • [Garn] Garnett, J. B., Bounded Analytic Functions, Academic Press, New York-London, 1981.
  • [Hal] Halmos, P. R., Shifts on Hilbert spaces. J. Reine Angew. Math., 208 (1961), 102–112.
  • [Hed1] Hedenmalm, H., A factorization theorem for square area-integrable functions. J. Reine Angew. Math., 422 (1991), 45–68.
  • [Hed2]—, A factoring theorem for the Bergman space. Bull. London Math. Soc., 26 (1994), 113–126.
  • [Her] Herrero, D., On multicyclic operators. Integral Equations Operator Theory, 1 (1978), 57–102.
  • [HKZ] Hedenmalm, H., Korenblum, B. & Zhu, K., Beurling type invariant subspaces of the Bergman space. J. London Math. Soc (2), 53 (1996), 601-614.
  • [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.
  • [Koo] Koosis, P., Introduction to Hp Spaces. Cambridge Univ. Press, New York, 1980.
  • [Kor] Korenblum, B., Outer functions and cyclic elements in Bergman spaces. J. Funct. Anal., 115 (1993), 104–118.
  • [KS] Khavinson, D. & Shapiro, H. S., Invariant subspaces in Bergman spaces and Hedenmalm's boundary value problem. Ark. Mat., 32 (1994), 309–321.
  • [M] Mirsky, L., An Introduction to Linear Algebra. Oxford Univ. Press, 1963.
  • [R] Richter, S., Invariant subspaces of the Dirichlet shift. J. Reine Angew. Math., 386 (1988), 205–220.
  • [S1] Shapiro, H. S., Weighted polynomial approximation and boundary behaviour of analytic functions, in Contemporary Problems in Analytic Functions (Erevan, 1965). Nauka, Moscow, 1966.
  • [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.