UNIVERSAL OVERCONVERGENCE AND OSTROWSKI-GAPS

J. MÜLLER; V. VLACHOU; A. YAVRIAN

doi:10.1112/S0024609306018492

Abstract

We prove that certain universality properties of the partial sums force a power series to have Ostrowski-gaps. This has interesting consequences for some classes of universal functions.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Costakis, George and Vlachou, Vagia 2006. Universal Taylor series on non-simply connected domains. Analysis, Vol. 26, Issue. 3,

Koumoullis, G. Luh, W. and Nestoridis, V. 2007. Universal functions are automatically universal in the sense of Menchoff. Complex Variables and Elliptic Equations, Vol. 52, Issue. 4, p. 307.

Costakis, George and Vlachou, Vagia 2007. Universal Taylor series on non-simply connected domains. Analysis, Vol. 26, Issue. 3, p. 347.

Trong, Dang Duc and Truong, Tuyen Trung 2008. The growth at infinity of a sequence of entire functions of bounded orders. Complex Variables and Elliptic Equations, Vol. 53, Issue. 8, p. 717.

Müller, J. Vlachou, V. and Yavrian, A. 2008. Overconvergent series of rational functions and universal Laurent series. Journal d'Analyse Mathématique, Vol. 104, Issue. 1, p. 235.

Bayart, Frédéric and Nestoridis, Vassili 2008. Universal Taylor series have a strong form of universality. Journal d'Analyse Mathématique, Vol. 104, Issue. 1, p. 69.

Gardiner, Stephen J. and Tsirivas, Nikolaos 2010. Universal Taylor series for non-simply connected domains. Comptes Rendus. Mathématique, Vol. 348, Issue. 9-10, p. 521.

Gardiner, Stephen J. 2012. Existence of Universal Taylor Series for Nonsimply Connected Domains. Constructive Approximation, Vol. 35, Issue. 2, p. 245.

Mouze, Augustin Nestoridis, Vassili Papadoperakis, Ioannis and Tsirivas, Nikolaos 2012. Determination of a Universal Series. Computational Methods and Function Theory, Vol. 12, Issue. 1, p. 173.

Manolaki, Myrto 2012. Ostrowski-type theorems for harmonic functions. Journal of Mathematical Analysis and Applications, Vol. 391, Issue. 2, p. 480.

Kyrezi, I. Nestoridis, V. and Papachristodoulos, C. 2012. Some remarks on abstract Universal series. Journal of Mathematical Analysis and Applications, Vol. 387, Issue. 2, p. 878.

Gardiner, Stephen J. and Khavinson, Dmitry 2013. Boundary behaviour of universal Taylor series. Comptes Rendus. Mathématique, Vol. 352, Issue. 2, p. 99.

Manolaki, Myrto 2013. Universal Polynomial Expansions of Harmonic Functions. Potential Analysis, Vol. 38, Issue. 3, p. 985.

Kalmes, Thomas Müller, Jürgen and Nieß, Markus 2013. On the behaviour of power series in the absence of Hadamard–Ostrowski gaps. Comptes Rendus. Mathématique, Vol. 351, Issue. 7-8, p. 255.

Gardiner, Stephen J. and Manolaki, Myrto 2014. Boundary Behaviour of Universal Taylor Series on Multiply Connected Domains. Constructive Approximation, Vol. 40, Issue. 2, p. 259.

Nestoridis, Vassili 2014. Universal Laurent series on domains of infinite connectivity. Proceedings of the American Mathematical Society, Vol. 142, Issue. 9, p. 3139.

Costakis, G. and Tsirivas, N. 2014. Doubly universal Taylor series. Journal of Approximation Theory, Vol. 180, Issue. , p. 21.

Daras, Nicholas J. and Nestoridis, Vassili 2015. Universal Taylor series on convex subsets of. Complex Variables and Elliptic Equations, Vol. 60, Issue. 11, p. 1567.

Gardiner, Stephen and Manolaki, Myrto 2015. A convergence theorem for harmonic measures with applications to Taylor series. Proceedings of the American Mathematical Society, Vol. 144, Issue. 3, p. 1109.

Gardiner, Stephen J. and Manolaki, Myrto 2016. Boundary behaviour of Dirichlet series with applications to universal series. Bulletin of the London Mathematical Society, Vol. 48, Issue. 5, p. 735.

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UNIVERSAL OVERCONVERGENCE AND OSTROWSKI-GAPS

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