Asymptotic properties of Müntz orthogonal polynomials

dc.contributor.advisor Lubinsky, Doron
dc.contributor.author Stefánsson, Úlfar F. en_US
dc.contributor.committeeMember Geronimo, Jeff
dc.contributor.committeeMember Heil, Christopher
dc.contributor.committeeMember Iliev, Plamen
dc.contributor.committeeMember Marcellan, Francisco
dc.contributor.department Mathematics en_US
dc.date.accessioned 2010-09-15T19:01:47Z
dc.date.available 2010-09-15T19:01:47Z
dc.date.issued 2010-05-12 en_US
dc.description.abstract Müntz 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.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/34759
dc.publisher Georgia Institute of Technology en_US
dc.subject Müntz polynomials en_US
dc.subject Müntz-Legendre polynomials en_US
dc.subject Asymptotic behavior en_US
dc.subject.lcsh Orthogonal polynomials Asymptotic theory
dc.title Asymptotic properties of Müntz orthogonal polynomials en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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