Otro
Distances between critical points and midpoints of zeros of hyperbolic polynomials
Registro en:
Bulletin Des Sciences Mathematiques. Paris: Gauthier-villars/editions Elsevier, v. 134, n. 2, p. 196-206, 2010.
0007-4497
10.1016/j.bulsci.2007.11.006
WOS:000275580900005
Autor
Dimitrov, Dimitar Kolev
Kostov, Vladimir P.
Resumen
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. Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)