Distances between critical points and midpoints of zeros of hyperbolic polynomials

Autor(es)

Dimitrov, Dimitar K. ^[1] ; Kostov, Vladimir P. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, IBILCE, Dept Ciencias Computacao & Estatist, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Nice, Math Lab, F-06108 Nice 2 - France

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN DES SCIENCES MATHEMATIQUES; v. 134, n. 2, p. 196-206, MAR 2010.
• Citações Web of Science: 1

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. (AU)

• Processo FAPESP: 03/01874-2 - Polinômios ortogonais e similares: propriedades e aplicações
• Beneficiário: Alagacone Sri Ranga
• Linha de fomento: Auxílio à Pesquisa - Temático