Doubly universal Taylor Series on simply connected domains

Chatzigiannakidou, Nikolitsa; Vlachou, Vagia

doi:10.48550/arxiv.1501.00878

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2015

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“…The methods in this paper come from potential theory. Potential Theory has recently become a powerful tool in solving a variety of problems on universal Taylor series; see the respective papers [5], [6], [8], [10] - [14], [17], [18], [19], [23], [25].…”

Section: Introductionmentioning

confidence: 99%

Universal Taylor series on specific compact sets

Tsirivas¹

2015

Preprint

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Let D be the unit disc. We denote by C the set of complex numbers and consider the setis endowed with the supremum norm. It is a well known result [20] that there exist holomorphic functions f on D for which the partial sums S n (f ), n = 1, 2, . . . of the Taylor series with center 0 are dense in A(K) for every K ∈ M D . It is also known that the above result fails [23] if we consider the weighted polynomials 2 n S n (f ), n = 1, 2, . . . instead of S n (f ), n = 1, 2, . . . . In the opposite direction, the main result of this work shows that there exist holomorphic functions f on D for which the sequence 2 n S n (f ), n = 1, 2, . . . is dense in A(K) for specific K ∈ M D . In this case the geometry of K plays a crucial role. We also generalize these results on arbitrary simply connected domains.

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Section: Introductionmentioning

confidence: 99%

Universal Taylor series on specific compact sets

Tsirivas¹

2015

Preprint

View full text Add to dashboard Cite

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Doubly universal Taylor Series on simply connected domains

Cited by 1 publication

References 4 publications

Universal Taylor series on specific compact sets

Universal Taylor series on specific compact sets

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