Polinômios ortogonais no círculo unitário associados a um par de sequências reais

• Autor(a) principal: SILVA, Roclilson Abreu da
• Data de Publicação: 2020
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFMA
• Texto Completo: https://tedebc.ufma.br/jspui/handle/tede/tede/4375
• topic: Medidas não triviais;; Polinômios ortogonais no círculo unitário;; Coeficientes de Verblunsky;; Sequências encadeadas;; Par de sequências reais.; Nontrivial measures;; Orthogonal polynomials on the unit cicle;; Verblunsky coefficients;; Chain sequences;; Pair of real sequences.; Matemática

In the theory of orthogonal polynomials on the unit circle, one of the main results is the well-known Verblunsky Theorem, in which, for any sequence of complex numbers, with modulus less than one, it is always possible to relate a nontrivial probability me- asure on the unit circle and, consequently, obtain its associated sequence of orthogonal polynomials (and vice versa). Based on this result, and on the theory of positive chain sequences, it was shown that is possible to obtain a characterization for these orthogonal polynomials on the unit circle in terms, now, of a pair of real sequences, where one of them is a positive chain sequence.