Complex Zero Decreasing Sequences

  title={Complex Zero Decreasing Sequences},
  author={Thomas M. Craven and George Csordas},
The purpose of this paper is to investigate the real sequences γ0, γ1, γ2, . . . with the property that if p(x) = ∑n k=0 akx k is any real polynomial, then ∑n k=0 γkakx k has no more nonreal zeros than p(x). In particular, the authors establish a converse to a classical theorem of Laguerre. 

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 21 references

A sufficient condition for all the roots of a polynomial to be real

  • D. C. Kurtz
  • Amer. Math. Monthly
  • 1992

Nørsett and E.B. Saff, On transformations and zeros of polynomials

  • S. P. INS A. Iserles
  • Rocky Mountain J. Math
  • 1991


  • F. Brenti
  • Log-concave and Pólya Frequency Sequences in…
  • 1989
1 Excerpt

Csordas , On the number of real roots of polynomials

  • G.
  • Pacific J . Math .
  • 1982

Zero-diminishing linear transformations

  • T. Craven, G. Csordas
  • Proc. Amer. Math. Soc
  • 1980


  • Pólya, Szegö, Problems, Theorems in Analysis
  • I and II, Springer-Verlag, New York,
  • 1976


  • Pólya, Collected Papers, Vol. II Location of Zeros
  • P. Boas, ed.), MIT Press, Cambridge, MA,
  • 1974

Collected Papers of G

  • G. H. Hardy
  • H. Hardy, vol. IV, Oxford Clarendon Press
  • 1969

Combinatorial Identities

  • J. Riordan
  • John Wiley, New York
  • 1968

Total Positivity

  • S. Karlin
  • vol. 1, Stanford Univ. Press, Stanford, Calif.
  • 1968

Similar Papers

Loading similar papers…