Linear Operators and the Distribution of Zeros of Entire Functions

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2007

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University of Hawaii at Manoa

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Abstract

Motivated by the work of Pólya, Schur, and Turán, a complete characterization of multiplier sequences for the Hermite polynomial basis is given. Laguerre's theorem and a remarkable curve theorem due to Pólya are generalized. Sufficient conditions for the location of zeros in certain strips in the complex plane are determined. Results pertaining to multiplier sequences and complex zero decreasing sequences for other polynomial sets are established.

Description

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Linear operators., Hermite polynomials.

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viii, 178 pages

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Theses for the degree of Doctor of Philosophy (University of Hawaii at Manoa). Mathematics ; no. 4887

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Table of Contents

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