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dc.contributor.authorAit-Haddou, Rachid
dc.date.accessioned2015-08-03T11:53:23Z
dc.date.available2015-08-03T11:53:23Z
dc.date.issued2014-05
dc.identifier.issn00219045
dc.identifier.doi10.1016/j.jat.2014.01.006
dc.identifier.urihttp://hdl.handle.net/10754/563514
dc.description.abstractWe show that the limiting polygon generated by the dimension elevation algorithm with respect to the Müntz space span(1,tr1,tr2,trm,. . .), with 0 < r1 < r2 < ⋯ < r m < ⋯ and lim n →∞r n = ∞, over an interval [a, b] ⊂ ] 0, ∞ [ converges to the underlying Chebyshev-Bézier curve if and only if the Müntz condition ∑i=1∞1ri=∞ is satisfied. The surprising emergence of the Müntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the convergence of the corresponding dimension elevation algorithms. The question of convergence with no condition of monotonicity or positivity on the pairwise distinct real numbers r i remains an open problem. © 2014 Elsevier Inc.
dc.publisherElsevier BV
dc.relation.urlhttp://arxiv.org/abs/arXiv:1309.0938v1
dc.subjectChebyshev blossoming
dc.subjectChebyshev-Bézier curves
dc.subjectChebyshev-Bernstein bases
dc.subjectDimension elevation
dc.subjectGelfond-Bernstein bases
dc.subjectMüntz spaces
dc.subjectSchur functions
dc.titleDimension elevation in Müntz spaces: A new emergence of the Müntz condition
dc.typeArticle
dc.contributor.departmentVisual Computing Center (VCC)
dc.identifier.journalJournal of Approximation Theory
dc.identifier.arxividarXiv:1309.0938
kaust.personAit-Haddou, Rachid
dc.date.posted2013-09-04


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