Acta Mathematica Hungarica

, Volume 137, Issue 4, pp 282–295 | Cite as

Multiplier sequences for simple sets of polynomials

  • T. Forgács
  • J. Tipton
  • B. Wright


We give a new characterization of simple sets of polynomials B with the property that the set of B-multiplier sequences contains all Q-multiplier sequences for every simple set Q. We characterize sequences of real numbers which are multiplier sequences for every simple set Q, and obtain some results toward the partitioning of the set of classical multiplier sequences.

Key words and phrases

partitioning multiplier sequences simple sets of polynomials 

Mathematics Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. Blakeman, E. Davis, T. Forgács and K. Urabe, On Legendre multiplier sequences, to appear in Missouri J. Math. Sci. Google Scholar
  2. [2]
    M. Chasse, Linear preservers and entire functions with restricted zero loci, Ph.D. dissertation, University of Hawai‘i at Manoa (2011). Google Scholar
  3. [3]
    T. Craven and G. Csordas, The Gauss–Lucas theorem and Jensen polynomials, Trans. Amer. Math. Soc., 278 (1983), 415–429. MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    T. Craven and G. Csordas, Location of zeros. I. Real polynomials and entire functions, Illinois J. Math., 27 (1983), 244–278. MathSciNetMATHGoogle Scholar
  5. [5]
    T. Forgács and A. Piotrowski, Multiplier sequences for generalized Laguerre bases, to appear in Rocky Mountain J. Math. Google Scholar
  6. [6]
    A. Piotrowski, Linear operators and the distribution of zeros of entire functions, Ph.D. dissertation, University of Hawai‘i at Manoa (2007). Google Scholar
  7. [7]
    G. Pólya and J. Schur, Über zwei Arten von Faktorenfolgen in der Theorie der algebraischen Gleichungen, J. Reine Angew. Math., 144 (1914), 89–113. MATHGoogle Scholar
  8. [8]
    G. Szegö, Orthogonal Polynomials, AMS Coll. Publ. XXIII (Providence, 1939). Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  1. 1.Department of MathematicsCalifornia State University, FresnoFresnoUSA
  2. 2.Department of MathematicsUniversity of IowaIowa CityUSA

Personalised recommendations