Extension operators for spaces of infinitely differentiable functions

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buir.advisorGoncharov, Alexander
dc.contributor.authorAltun, Muhammed
dc.date.accessioned2016-07-01T11:04:24Z
dc.date.available2016-07-01T11:04:24Z
dc.date.issued2005
dc.departmentDepartment of Mathematicsen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.description.abstractWe start with a review of known linear continuous extension operators for the spaces of Whitney functions. The most general approach belongs to PawÃlucki and Ple´sniak. Their operator is continuous provided that the compact set, where the functions are defined, has Markov property. In this work, we examine some model compact sets having no Markov property, but where a linear continuous extension operator exists for the space of Whitney functions given on these sets. Using local interpolation of Whitney functions we can generalize the PawÃlucki-Ple´sniak extension operator. We also give an upper bound for the Green function of domains complementary to generalized Cantor-type sets, where the Green function does not have the H¨older continuity property. And, for spaces of Whitney functions given on multidimensional Cantor-type sets, we give the conditions for the existence and non-existence of a linear continuous extension operator.en_US
dc.description.degreePh.D.en_US
dc.description.statementofresponsibilityAltun, Muhammeden_US
dc.format.extentviii, 63 leavesen_US
dc.identifier.itemidBILKUTUPB094217
dc.identifier.urihttp://hdl.handle.net/11693/29740
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectExtension operatoren_US
dc.subjectGreen functionen_US
dc.subjectMarkov inequalityen_US
dc.subjectInfinitely differentiable functionsen_US
dc.subjectPolynomial interpolationen_US
dc.subject.lccQA274.7 .A48 2005en_US
dc.subject.lcshMarkov processes.en_US
dc.titleExtension operators for spaces of infinitely differentiable functionsen_US
dc.typeThesisen_US
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