universal taylor series
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2021 ◽  
Vol 7 (2) ◽  
Author(s):  
K. Kioulafa ◽  
G. Kotsovolis ◽  
V. Nestoridis


Author(s):  
G. Gavrilopoulos ◽  
K. Maronikolakis ◽  
V. Nestoridis

AbstractWe establish generic existence of Universal Taylor Series on products $$\varOmega = \prod \varOmega _i$$ Ω = ∏ Ω i of planar simply connected domains $$\varOmega _i$$ Ω i where the universal approximation holds on products K of planar compact sets with connected complements provided $$K \cap \varOmega = \emptyset $$ K ∩ Ω = ∅ . These classes are with respect to one or several centers of expansion and the universal approximation is at the level of functions or at the level of all derivatives. Also, the universal functions can be smooth up to the boundary, provided that $$K \cap \overline{\varOmega } = \emptyset $$ K ∩ Ω ¯ = ∅ and $$\{\infty \} \cup [{\mathbb {C}} {\setminus } \overline{\varOmega }_i]$$ { ∞ } ∪ [ C \ Ω ¯ i ] is connected for all i. All previous kinds of universal series may depend on some parameters; then the approximable functions may depend on the same parameters, as it is shown in the present paper.





2018 ◽  
Vol 44 (2) ◽  
pp. 237-249
Author(s):  
V. Nestoridis


Author(s):  
Evgeny Abakumov ◽  
Jürgen Müller ◽  
Vassili Nestoridis


2016 ◽  
Vol 86 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Luis Bernal-González ◽  
Andreas Jung ◽  
Jürgen Müller


2016 ◽  
Vol 2 (4) ◽  
pp. 1031-1038 ◽  
Author(s):  
Nicky Chatzigiannakidou ◽  
Vagia Vlachou


2016 ◽  
Vol 59 (1) ◽  
pp. 109-117 ◽  
Author(s):  
A. MOUZE ◽  
V. MUNNIER

AbstractWe prove that the classical universal Taylor series in the complex plane are never frequently universal. On the other hand, we prove the 1-upper frequent universality of all these universal Taylor series.



2016 ◽  
Vol 284 (3-4) ◽  
pp. 919-946 ◽  
Author(s):  
Augustin Mouze ◽  
Vincent Munnier


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