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Periodica Mathematica Hungarica

, Volume 71, Issue 2, pp 250–260 | Cite as

On the characteristic polynomials of linear functional equations

  • Cs. VinczeEmail author
  • A. Varga
Article

Abstract

The solutions of a linear functional equation are typically generalized polynomials. The existence of their non-trivial monomial terms strongly depends on the algebraic properties of some related families of parameters. In extremal cases (the parameters are algebraic numbers or the parameters form an algebraically independent system) we have elegant methods to decide the existence of non-trivial solutions. In this paper we are going to extend and unify the treatment of the existence problem by introducing the characteristic polynomials of a linear functional equation such that the algebraic properties of the roots allows us to conclude the existence of non-trivial solutions.

Keywords

Linear functional equations Spectral analysis Field homomorphisms 

Mathematics Subject Classification

39B22 

Notes

Acknowledgments

Cs. Vincze was partially supported by the European Union and the European Social Fund through the project Supercomputer, the national virtual lab (Grant No.:TÁMOP-4.2.2.C-11/1/KONV-2012-0010). The work is supported by the University of Debrecen’s internal research Project RH/885/2013.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2015

Authors and Affiliations

  1. 1.University of DebrecenDebrecenHungary

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