Opuscula Math. 35, no. 6 (2015), 957-972
http://dx.doi.org/10.7494/OpMath.2015.35.6.957

 
Opuscula Mathematica

Nontrivial solutions of linear functional equations: methods and examples

Adrienn Varga
Csaba Vincze

Abstract. For a wide class of linear functional equations the solutions are generalized polynomials. The existence of non-trivial monomial terms of the solution strongly depends on the algebraic properties of some related families of parameters. As a continuation of the previous work [A. Varga, Cs. Vincze, G. Kiss, Algebraic methods for the solution of linear functional equations, Acta Math. Hungar.] we are going to present constructive algebraic methods of the solution in some special cases. Explicit examples will be also given.

Keywords: linear functional equations, spectral analysis, field homomorphisms.

Mathematics Subject Classification: 39B22.

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  • Adrienn Varga
  • University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
  • Csaba Vincze
  • University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary
  • Received: 2014-08-28.
  • Revised: 2014-12-15.
  • Accepted: 2014-12-16.
Opuscula Mathematica - cover

Cite this article as:
Adrienn Varga, Csaba Vincze, Nontrivial solutions of linear functional equations: methods and examples, Opuscula Math. 35, no. 6 (2015), 957-972, http://dx.doi.org/10.7494/OpMath.2015.35.6.957

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