Some examples of cyclic vectors in the Dirichlet space
HTML articles powered by AMS MathViewer
- by Leon Brown and William Cohn PDF
- Proc. Amer. Math. Soc. 95 (1985), 42-46 Request permission
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
- Leon Brown and Allen L. Shields, Cyclic vectors in the Dirichlet space, Trans. Amer. Math. Soc. 285 (1984), no. 1, 269–303. MR 748841, DOI 10.1090/S0002-9947-1984-0748841-0
- Lennart Carleson, Sets of uniqueness for functions regular in the unit circle, Acta Math. 87 (1952), 325–345. MR 50011, DOI 10.1007/BF02392289
- Lennart Carleson, Selected problems on exceptional sets, Van Nostrand Mathematical Studies, No. 13, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0225986
- Jean-Pierre Kahane and Raphaël Salem, Ensembles parfaits et séries trigonométriques, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1301, Hermann, Paris, 1963 (French). MR 0160065
Additional Information
- © Copyright 1985 American Mathematical Society
- 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