Publicação: Distances between critical points and midpoints of zeros of hyperbolic polynomials
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Data
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Coorientador
Pós-graduação
Curso de graduação
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ISSN da Revista
Título de Volume
Editor
Gauthier-villars/editions Elsevier
Tipo
Artigo
Direito de acesso
Acesso restrito
Resumo
Let p(x) be a polynomial of degree n with only real zeros x(1) <= x(2) <= ... <= x(n). Consider their midpoints z(k) = (x(k) + x(k+1))/2 and the zeros xi(1) <= xi(2) <= ... <= xi(n-1) of p'(z). Motivated by a question posed by D. Farmer and R. Rhoades, we compare the smallest and largest distances between consecutive xi(k) to the ones between consecutive z(k). The corresponding problem for zeros and critical points of entire functions of order one from the Laguerre-Polya class is also discussed. (C) 2007 Published by Elsevier Masson SAS.
Descrição
Palavras-chave
Hyperbolic polynomial, Strictly hyperbolic polynomial, Zero, Midpoint, Critical point, Entire function, Laguerre-Polya class
Idioma
Inglês
Como citar
Bulletin Des Sciences Mathematiques. Paris: Gauthier-villars/editions Elsevier, v. 134, n. 2, p. 196-206, 2010.
