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A Liouville-type result for lacunary power series and converse results for universal holomorphic functions
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Valeri A. Martirosian
Published/Copyright:
September 25, 2009
A Liouville-type result is proved for holomorphic functions having lacunary power series with restricted growth for a subsequence of the partial sums. As an application, converse results concerning existence of universal holomorphic functions are given.
Received: 2006-1-14
Published Online: 2009-9-25
Published in Print: 2006-9-1
© Oldenbourg Wissenschaftsverlag
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Articles in the same Issue
- Universal overconvergence of homogeneous expansions of harmonic functions
- Joint universality for sums and products of Dirichlet L-functions
- On the speed of convergence to limit distributions for Hecke L-functions associated with ideal class characters
- Universal Taylor series on unbounded open sets
- Universality for generalized Euler products
- Universal Taylor series on non-simply connected domains
- Compositional universality in the N-dimensional ball
- A discrete universality theorem for general Dirichlet series
- On the zeros of T-universal functions
- A Liouville-type result for lacunary power series and converse results for universal holomorphic functions
- Universal Taylor series on open subsets of Rn
- A universal harmonic function which is bounded on each line
- The joint universality for periodic Hurwitz zeta-functions
