Zero sets of bivariate Hermite polynomials

dc.contributorUniversidade Estadual Paulista (UNESP)
dc.creatorArea, Ivan
dc.creatorDimitrov, Dimitar K.
dc.creatorGodoy, Eduardo
dc.date2015-10-21T13:14:41Z
dc.date2016-10-25T21:00:38Z
dc.date2015-10-21T13:14:41Z
dc.date2016-10-25T21:00:38Z
dc.date2015-01-01
dc.date.accessioned2017-04-06T09:01:54Z
dc.date.available2017-04-06T09:01:54Z
dc.identifierJournal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 421, n. 1, p. 830-841, 2015.
dc.identifier0022-247X
dc.identifierhttp://hdl.handle.net/11449/128864
dc.identifierhttp://acervodigital.unesp.br/handle/11449/128864
dc.identifierhttp://dx.doi.org/10.1016/j.jmaa.2014.07.042
dc.identifierWOS:000349939100049
dc.identifierhttp://www.sciencedirect.com/science/article/pii/S0022247X14006854
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/939420
dc.descriptionWe 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.
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.languageeng
dc.publisherElsevier B.V.
dc.relationJournal Of Mathematical Analysis And Applications
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectBivariate Hermite polynomials
dc.subjectZero sets of bivariate polynomials
dc.subjectBivariate Gaussian distribution
dc.subjectBivariate orthogonal polynomials
dc.subjectHermite polynomials
dc.subjectAlgebraic plane curves
dc.titleZero sets of bivariate Hermite polynomials
dc.typeOtro


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