Journal of the Australian Mathematical Society

Table of Contents - 2002 - Volume 72, Issue 01  

Research Article

The zeros of linear combinations of translates of polynomials

Peter Walkera1

a1 College of Arts and Science, American University of Sharjah, P.O. 26666 Sharjah, United Arab Emirates e-mail: peterw@aus.ac.ae

Abstract

We investigate the location and separation of zeros of certain three-term linear combination of translates of polynomials. In particular, we find an interval of the form I = [−1, 1 + h], h > 0 such that for a polynomial f, all of whose zeros are real, and λ xs2208 I, all zeros of f (x + 2ic) + 2λf (x) + f (x – 2ic) are also real.

(Received September 26 2000)

(Revised February 07 2001)

2000 Mathematics subject classification

  • primary 26C10;
  • 30C15