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dc.contributor.authorStefánsson, Úlfar F.en_US
dc.date.accessioned2010-09-15T19:01:47Z
dc.date.available2010-09-15T19:01:47Z
dc.date.issued2010-05-12en_US
dc.identifier.urihttp://hdl.handle.net/1853/34759
dc.description.abstractMüntz polynomials arise from consideration of Müntz's Theorem, which is a beautiful generalization of Weierstrass's Theorem. We prove a new surprisingly simple representation for the Müntz orthogonal polynomials on the interval of orthogonality, and in particular obtain new formulas for some of the classical orthogonal polynomials (e.g. Legendre, Jacobi, Laguerre). This allows us to determine the strong asymptotics and endpoint limit asymptotics on the interval. The zero spacing behavior follows, as well as estimates for the smallest and largest zeros. This is the first time that such asymptotics have been obtained for general Müntz exponents. We also look at the asymptotic behavior outside the interval and the asymptotic properties of the associated Christoffel functions.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectMüntz polynomialsen_US
dc.subjectMüntz-Legendre polynomialsen_US
dc.subjectAsymptotic behavioren_US
dc.subject.lcshOrthogonal polynomials Asymptotic theory
dc.titleAsymptotic properties of Müntz orthogonal polynomialsen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Lubinsky, Doron; Committee Member: Geronimo, Jeff; Committee Member: Heil, Christopher; Committee Member: Iliev, Plamen; Committee Member: Marcellan, Franciscoen_US


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