The capacity of sets of divergence of Certain Taylor Series on the unit circle

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dc.contributor.author Twomey, J. Brian
dc.date.accessioned 2019-08-22T15:30:02Z
dc.date.available 2019-08-22T15:30:02Z
dc.date.issued 2019-05-09
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 en
dc.identifier.volume 19 en
dc.identifier.issued 2 en
dc.identifier.startpage 227 en
dc.identifier.endpage 236 en
dc.identifier.uri http://hdl.handle.net/10468/8382
dc.identifier.doi 10.1007/s40315-019-00266-z en
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. en
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher Springer en
dc.relation.uri https://link.springer.com/article/10.1007%2Fs40315-019-00266-z
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 en
dc.subject Convergence of Taylor series en
dc.subject Trigonometric series en
dc.subject Capacity en
dc.subject Exceptional sets en
dc.subject Dirichlet-type spaces en
dc.subject Analytic Besov spaces en
dc.title The capacity of sets of divergence of Certain Taylor Series on the unit circle en
dc.type Article (peer-reviewed) en
dc.internal.authorcontactother Brian Twomey, School Of Mathematical Sciences, University College Cork, Cork, Ireland. +353-21-490-3000 Email: b.twomey@ucc.ie en
dc.internal.availability Full text available en
dc.check.info Access to this article is restricted until 12 months after publication by request of the publisher. en
dc.check.date 2020-05-09
dc.description.version Accepted Version en
dc.description.status Peer reviewed en
dc.identifier.journaltitle Computational Methods and Function Theory en
dc.internal.IRISemailaddress b.twomey@ucc.ie en


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