Vagia Vlachou

UNIVERSAL OVERCONVERGENCE AND OSTROWSKI-GAPS

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.

A Universal Taylor Series in the Doubly Connected Domain C\{1}

We give a constructive proof of the existence of a universal Taylor series with center 0 in the doubly connected domain C\{1}. We also obtain a residuality result.

Universal Taylor series on non-simply connected domains

In the present paper, we investigate the existence of universal Taylor series on certain non-simply connected domains. Moreover, we prove that Hadamard-Ostrowski gaps is a generic property in the space of holomorphic functions on a doubly connected domain.

Universal Faber Series with Hadamard-Ostrowski Gaps

For certain non-simply connected domains of even infinite connectivity, we prove that there exist holomorphic functions such that a) their Faber expansions with respect to suitable compact sets Γ have approximating properties outside their domain of holomorphy, and b) the coefficients of the Faber expansions have the property of Hadamard-Ostrowski gaps.

Identical approximative sequence for various notions of Universality

In this paper, we examine various notions of universality, which have already been proved generic. Our main purpose is to prove that generically they occur simultaneously with the same approximative sequence.

Coincidence of Two Classes of Universal Laurent Series

There exist functions, called U.L.S. (Universal Laurent Series), holomorphic on finitely connected domains Ω in C, whose Laurent-type partial sums approximate everything we can hope for, on compact subsets outside Ω ∪ {a 1,…,a}, for certain prescribed points a 1,…,a k. In this paper we prove that, under additional assumptions, for every U.L.S. there exists a subsequence of its Laurent-type partial sums, which converges to the function itself in the whole of Ω and which approximates everything we can hope for outside Ω ∪ {a 1,…,a, k}.

Construction of a Universal Laurent Series

Let Ω be a finitely connected domain. We prove constructively the existence of a universal Laurent series, that is, a holomorphic function f on Ω having universal approximation properties connected with partial sums of Taylor and Laurent expansions.

Smooth universal Taylor series on doubly connected domains

We prove the existence of universal Taylor series on certain doubly connected domains, which are smooth on a part of the boundary. We also prove that such functions may vanish at . These results are presented for universal Taylor series with respect to one centre and with respect to all possible centres.