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Some examples of cyclic vectors in the Dirichlet space


Authors: Leon Brown and William Cohn
Journal: Proc. Amer. Math. Soc. 95 (1985), 42-46
MSC: Primary 30D35; Secondary 30H05, 47B38
DOI: https://doi.org/10.1090/S0002-9939-1985-0796443-9
MathSciNet review: 796443
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Abstract: We consider the Hilbert space of analytic functions in the open unit disc that have a finite Dirichlet integral. For $ E$, a closed subset of the unit circle with logarithmic capacity zero, we construct a function in this space which is uniformly continuous, vanishes on $ E$, and is cyclic with respect to the shift operator.


References [Enhancements On Off] (What's this?)

  • [1] L. Brown and A. L. Shields, Cyclic vectors in the Dirichlet space, Trans. Amer. Math. Soc. 285 (1984), 269-304. MR 748841 (86d:30079)
  • [2] L. Carleson, Sets of uniqueness for functions regular in the unit circle, Acta Math. 87 (1952), 325-345. MR 0050011 (14:261a)
  • [3] -, Selected problems on exceptional sets, Van Nostrand, Princeton, N.J., 1967. MR 0225986 (37:1576)
  • [4] J.-P. Kahane and R. Salem, Ensembles parfaits et śeries trigonométriques, Actualités Sci. Indust., no. 1301, Hermann, Paris, 1963. MR 0160065 (28:3279)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0796443-9
Keywords: Hilbert space of analytic functions, Dirichlet integral, cyclic vectors, logarithmic capacity
Article copyright: © Copyright 1985 American Mathematical Society

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