Inner functions and cyclic vectors in the Bloch space

  title={Inner functions and cyclic vectors in the Bloch space},
  author={J. Milne Anderson and J. L. Fern{\aa}ndez and Allen L. Shields},
  journal={Transactions of the American Mathematical Society},
In this paper we construct a singular inner function whose polynomial multiples are dense in the little Bloch space qo . 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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In these three lectures we consider Banach spaces of analytic functions on plane domains. If the space admits the operator of multiplication by z, then it is of interest to describe the cyclic
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This result was conjectured by A. E. Taylor in 1951 (see [7, p. 33]). The analogous proposition for two-sided sequences ...*, a-i, ao, a,, * * * }, with the space HX of bounded analytic functions
The second duals of certain spaces of analytic functions
  • L. Rubel, A. Shields
  • Mathematics, Philosophy
    Journal of the Australian Mathematical Society
  • 1970
Let ϕ be a continuous, decreasing, real-valued funtion on 0 ≦ r ≦ 1 with ϕ(1) = 0 and ϕ(r) > 0 for r < 1. Let E0 be the Banach space of analytic function f on the open unit disc D, such that
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DEFINITIONS. 1. A~ (p > 0) is the Banach space of analytic functions f(z) in U = {z G C| \z\ < 1} that satisfy \f(z)\ = o[(l \z\)~] (\z\ > 1) with the norm \\f\\ = max{ |f(z)\(l z)} (z G If). Note
The space of bounded analytic functions on a region
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