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
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
- Communicated by Karol Baron.
- Received: 2014-08-28.
- Revised: 2014-12-15.
- Accepted: 2014-12-16.
- Published online: 2015-06-06.
