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Universal Taylor series on open subsets of Rn
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George Costakis
Published/Copyright:
September 25, 2009
In the case of the complex plane, several notions of universal Taylor series have been introduced, ([10, 2, 19, 20]). The purpose of the present article is to establish the existence of universal Taylor series of C∞ functions in general open subsets of the Euclidean space Rn, n ≥ 1.
Received: 2006-1-1
Accepted: 2006-4-16
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
