Growth of coefficients of universal Taylor series and comparison of two classes of functions

Melas, Antonios D.; Nestoridis, Vassili; Papadoperakis, Ioannis

doi:10.1007/bf02788143

Cited by 44 publications

(71 citation statements)

References 5 publications

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“…If |z 0 | = R 2 we observe that ∞ l=1 c −l z −l 0 converges and that ∞ l=0 c k z l ∈ U (D R2 ), and then, using the corresponding property of a universal Taylor series on a disc [7,8], the result follows.…”

Section: Remark 33 For Everymentioning

confidence: 83%

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Universal Laurent Series

Costakis

Nestoridis²,

Papadoperakis³

2005

Proceedings of the Edinburgh Mathematical Society

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Section: Remark 33 For Everymentioning

confidence: 83%

“…Furthermore, some properties of such universal Taylor series have been investigated in [6][7][8]11]. …”

Section: Introductionmentioning

confidence: 99%

Universal Laurent Series

Costakis

Nestoridis²,

Papadoperakis³

2005

Proceedings of the Edinburgh Mathematical Society

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“…K ∩ Ω = ∅, then we have the definitions of the corresponding classes and Functional Analysis we refer to [14,15]. Properties of the universal functions belonging to these classes can be found in [1,2,4,[9][10][11][12]16,19,[23][24][25][26][27][28]30,31]. For example, 26]).…”

Section: Definition 12mentioning

confidence: 99%

Coincidence of some classes of universal functions

Katsoprinakis¹

2009

Rev. Mat. Complut.

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Let Ω be a domain in the complex plane such that Ω satisfies appropriate geometrical and topological properties. We prove that if f is a holomorphic function in Ω, then its Taylor series, with center at any ξ ∈ Ω, is universal with respect to overconvergence if and only if its Cesàro (C, k)-means are universal for any real k > −1. This is an extension of the same result, proved recently by F. Bayart, for any integer k ≥ 0. As a consequence, several classes of universal functions introduced in the related literature are shown to coincide.

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“…Note that [6] contains the result that any Universal Taylor series cannot belong to the class N of Nevanlinna, thus implying the last part of our Theorem 3. But since the method of proof is different and since it may have some independent interest we include it here.…”

Section: An Applicationmentioning

confidence: 91%

“…Now we shall make some comments for the class of Universal Taylor Series. As we mentioned before, several questions arise naturally about this class of series (see [3], [4], [6] and [7]). Although some of them have been answered, there are others which remain open.…”

Section: Remarks and Commentsmentioning

confidence: 99%