Orientadores: Dimitar Kolev Dimitrov, Roberto Andreani / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-15T04:39:55Z (GMT). No. of bitstreams: 1 Rafaeli_FernandoRodrigo_D.pdf: 1231425 bytes, checksum: 33a23775a69f9b2b36c516f7cfcb0d0f (MD5) Previous issue date: 2010 / Resumo: Neste trabalho são obtidos resultados sobre o comportamento de zeros de polinômios ortogonais. Sabe-se que todos eles são reais e distintos e fazem papel importante de nós das mais utilizadas fórmulas de integração numérica, que são as fórmulas de quadratura de Gauss. São obtidos resultados sobre a localização e a monotonicidade dos zeros, considerados como funções dos correspondentes parâmetros, dos polinômios ortogonais clássicos. Apresentaremos também vários resultados que tratam da localização, monotonicidade e da assintótica de zeros de certas classes de polinômios ortogonais relacionados com as medidas clássicas / Abstract: Results concerning the behaviour of zeros of orthogonal polynomials are obtained. It is known that they are real and distinct and play as important role as node of the most frequently used rules for numerical integration, the Gaussian quadrature formulae. Result about the location and monotonicity of the zeros, considered as functions of parameters involved in the measure, are provided. We present various results that treat questions about location, monotonicity and asymptotics of zeros of certain classes of orthogonal polynomials with respect to measure that are closely related to the classical ones / Doutorado / Analise Aplicada / Doutor em Matemática Aplicada

A dissertation submitted to the Faculty of Science, School of Mathematics University of the Witwatersrand Johannesburg South Africa / Linear second order ordinary di erential boundary value problems feature prominently in many scienti c eld, such as physics and engineering. Solving these problems is often riddled with complications though a myriad of techniques have been devised to alleviate these di culties. One such method is by transforming a problem into a more readily solvable form or a problem which behaves in a manner which is well understood. The Darboux-Crum transformation is a particularly interesting transformation characterised by some surprising properties, and an increase in the number of works produced in the last few years related to this transformation has prompted this investigation. The classical orthogonal polynomials, namely those of Jacobi, Legendre, Hermite and Laguerre, have been nominated as test candidates and this work will investigate how these orthogonal families are a ected when transformed via Darboux-Crum transformations.

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A research report submitted to the Faculty of Science, University of the Witwatersrand, in partial fulfillment of the degree of Master of Science. / The Toeplitz form is a most useful and important teo! in many areas of applied. mathematics today including signal processing, time-series analysis and prediction theory. It is even used in quantum mechanics in Ising model correlation functions. (Abbreviation abstract) / AC 2018

The classical moment problem concerns distribution functions on the real line. The central feature is the connection between distribution functions and the moment sequences which they generate via a Stieltjes integral. The solution of the classical moment problem leads to the well known theorem of Favard which connects orthogonal polynomial sequences with distribution functions on the real line. Orthogonal polynomials in their turn arise in the computation of measures via continued fractions and the Nevanlinna parametrisation. In this dissertation classical orthogonal polynomials are investigated rst and their connection with hypergeometric series is exhibited. Results from the moment problem allow the study of a more general class of orthogonal polynomials. q-Hypergeometric series are presented in analogy with the ordinary hypergeometric series and some results on q-Laguerre polynomials are given. Finally recent research will be discussed.

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [95]-100)

Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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Orientador: Eliana Xavier Linhares de Andrade / Banca: Sérgio Antonio Tozoni / Banca: Dimitar Kolev Dimitrov / Resumo: O principal objetivo deste trabalho é estudar um problema de eletrostática geral que envolve ambos, um campo externo e restrições sobre cargas livres. Foram fornecidas condições necessárias e suficientes para o mínimo da energia em termos de soluções polinomiais de uma equação diferencial de Lamé modificada. Além disso, foram dadas novas demonstrações, mais simples, de resultados clássicos de Stieltjes e Szego. Finalmente, foi obtida uma interpretação eletrostática para os zeros dos polinômios comumente chamados de Hermite-Laurent. / Abstract: A general electrostatic problem which involves both an external field and restrictions on the free charges is studied. Necessary and sufficient conditions for the minimum of the energy are furnished in terms of polynomial solutions of a modified Lamé differential equation. New simplified proofs of classical results of Sitieltjes and Szego are given. An electrostatic interpretation of the so-called Hermite-Laurent polynomials is obtained. / Mestre