dc.contributor.author |
Twomey, J. Brian |
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dc.date.accessioned |
2019-08-22T15:30:02Z |
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dc.date.available |
2019-08-22T15:30:02Z |
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dc.date.issued |
2019-05-09 |
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dc.identifier.citation |
Twomey, J. B. (2019) 'The Capacity of Sets of Divergence of Certain Taylor Series on the Unit Circle', Computational Methods and Function Theory, 19(2), pp. 227-236. doi: 10.1007/s40315-019-00266-z |
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dc.identifier.volume |
19 |
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dc.identifier.issued |
2 |
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dc.identifier.startpage |
227 |
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dc.identifier.endpage |
236 |
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dc.identifier.uri |
http://hdl.handle.net/10468/8382 |
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dc.identifier.doi |
10.1007/s40315-019-00266-z |
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dc.description.abstract |
A simple and direct proof is given of a generalization of a classical result on the convergence of ∑∞k=0ak e ikx outside sets of x of an appropriate capacity zero, where f(z)=∑∞k=0akzk is analytic in the unit disc U and ∑∞k=0kα|ak|2<∞ with α∈(0,1]. We also discuss some convergence consequences of our results for weighted Besov spaces, for the classes of analytic functions in U for which ∑∞k=1kγ|ak|p<∞, and for trigonometric series of the form ∑∞k=1(αkcoskx+βksinkx) with ∑∞k=1kγ(|αk|p+|βk|p)<∞ , where γ>0,p>1. |
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dc.format.mimetype |
application/pdf |
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dc.language.iso |
en |
en |
dc.publisher |
Springer |
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dc.relation.uri |
https://link.springer.com/article/10.1007%2Fs40315-019-00266-z |
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dc.rights |
© Springer-Verlag GmbH Germany, part of Springer Nature 2019. This is a post-peer-review, pre-copyedit version of an article published in Computational Methods and Function Theory. The final authenticated version is available online at: http://dx.doi.org/10.1007/s40315-019-00266-z |
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dc.subject |
Convergence of Taylor series |
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dc.subject |
Trigonometric series |
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dc.subject |
Capacity |
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dc.subject |
Exceptional sets |
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dc.subject |
Dirichlet-type spaces |
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dc.subject |
Analytic Besov spaces |
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dc.title |
The capacity of sets of divergence of Certain Taylor Series on the unit circle |
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dc.type |
Article (peer-reviewed) |
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dc.internal.authorcontactother |
Brian Twomey, School Of Mathematical Sciences, University College Cork, Cork, Ireland. +353-21-490-3000 Email: b.twomey@ucc.ie |
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dc.internal.availability |
Full text available |
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dc.check.info |
Access to this article is restricted until 12 months after publication by request of the publisher. |
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dc.check.date |
2020-05-09 |
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dc.description.version |
Accepted Version |
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dc.description.status |
Peer reviewed |
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dc.identifier.journaltitle |
Computational Methods and Function Theory |
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dc.internal.IRISemailaddress |
b.twomey@ucc.ie |
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