Inner functions and cyclic vectors in the Bloch space

Anderson, J. M.; Fernández, J. L.; Shields, A. L.

doi:10.1090/S0002-9947-1991-0979966-6

Inner functions and cyclic vectors in the Bloch space
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by J. M. Anderson, J. L. Fernández and A. L. Shields

Trans. Amer. Math. Soc. 323 (1991), 429-448

DOI: https://doi.org/10.1090/S0002-9947-1991-0979966-6

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Abstract:

In this paper we construct a singular inner function whose polynomial multiples are dense in the little Bloch space ${\mathcal {B}_0}$. To do this we construct a singular measure on the unit circle with "best possible" control of both the first and second differences.

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Cyclic inner functions in Bergman spaces

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