Zero sets of bivariate Hermite polynomials
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Data
2015-01-01
Autores
Area, Ivan
Dimitrov, Dimitar K. [UNESP]
Godoy, Eduardo
Título da Revista
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Editor
Elsevier B.V.
Resumo
We establish various properties for the zero sets of three families of bivariate Hermite polynomials. Special emphasis is given to those bivariate orthogonal polynomials introduced by Hermite by means of a Rodrigues type formula related to a general positive definite quadratic form. For this family we prove that the zero set of the polynomial of total degree n + m consists of exactly n + m disjoint branches and possesses n + m asymptotes. A natural extension of the notion of interlacing is introduced and it is proved that the zero sets of the family under discussion obey this property. The results show that the properties of the zero sets, considered as affine algebraic curves in R-2, are completely different for the three families analyzed. (c) 2014 Elsevier Inc. All rights reserved.
Descrição
Palavras-chave
Bivariate Hermite polynomials, Zero sets of bivariate polynomials, Bivariate Gaussian distribution, Bivariate orthogonal polynomials, Hermite polynomials, Algebraic plane curves
Como citar
Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 421, n. 1, p. 830-841, 2015.