Advertisement

Ukrainian Mathematical Journal

, Volume 45, Issue 10, pp 1481–1489 | Cite as

On sequences that do not increase the number of real roots of polynomials

  • A. G. Bakan
  • A. P. Golub
Article

Abstract

A complete description is given for the sequences {λk} k=0 such that, for an arbitrary real polynomial\(f(t) = \sum\nolimits_{k = 0}^n {a_k t^k } \), an arbitraryA ε (0,+∞), and a fixedC ε (0,+∞), the number of roots of the polynomial\((Tf)(t) = \sum\nolimits_{k = 0}^n {a_k \lambda _k t^k } \) on [0,C] does not exceed the number of roots off(t) on [0,A].

Keywords

Real Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Karlin,Total Positivity, Vol. 1, Stanford Univ. Press, Stanford (1968).Google Scholar
  2. 2.
    T. Graven and G. Csordas, “Zero-diminishing linear transformations,”Proc. Amer. Math. Soc.,80, No. 4, 544–546 (1980).Google Scholar
  3. 3.
    T. Graven and G. Csordas, “An inequality for the distribution of zeros of polynomials and entire functions,”Pacif. J. Math.,95, No. 2, 263–280 (1981).Google Scholar
  4. 4.
    T. Graven and G. Csordas, “On the number of real roots of polynomials,”Pacif. J. Math.,102, No. 1, 15–28 (1981).Google Scholar
  5. 5.
    T. Graven and G. Csordas, “Locations of zeros. Pt 1: Real polynomials and entire functions,”Pacif. J. Math.,27, No. 2, 244–278 (1983).Google Scholar
  6. 6.
    A. G. Bakan and A. P. Golub, “Some negative results on sequences of factors of the first kind,”Ukr. Mat. Zh.,44, No. 3, 305–309 (1992).Google Scholar
  7. 7.
    N. I. Akhiezer,The Classical Moment Problem and Some Related Problems in Analysis [in Russian], Fizmatgiz, Moscow (1961).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. G. Bakan
    • 1
  • A. P. Golub
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

Personalised recommendations