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The zeros of linear combinations of translates of polynomials

Part of: Geometric function theory Polynomials, rational functions

Published online by Cambridge University Press:  09 April 2009

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

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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 ∈ I, all zeros of f (x + 2ic) + 2λf (x) + f (x – 2ic) are also real.

MSC classification

Secondary: 26C10: Polynomials 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 109 - 118
Copyright
Copyright © Australian Mathematical Society 2002

References

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