Asymptotic properties of Müntz orthogonal polynomials

Show simple item record Stefánsson, Úlfar F. en_US 2010-09-15T19:01:47Z 2010-09-15T19:01:47Z 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.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 Dissertation en_US Ph.D. en_US
dc.contributor.department Mathematics en_US
dc.description.advisor Committee Chair: Lubinsky, Doron; Committee Member: Geronimo, Jeff; Committee Member: Heil, Christopher; Committee Member: Iliev, Plamen; Committee Member: Marcellan, Francisco en_US

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