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Acta Mathematica Hungarica

, Volume 146, Issue 1, pp 128–141 | Cite as

Algebraic methods for the solution of linear functional equations

  • G. Kiss
  • A. Varga
  • CS. VinczeEmail author
Article

Abstract

The equation
$$\sum^{n}_ {i=0} a_{i}f(b_{i}x + (1 - b_{i})y) = 0$$
belongs to the class of linear functional equations. The solutions form a linear space with respect to the usual pointwise operations. According to the classical results of the theory they must be generalized polynomials. New investigations have been started a few years ago. They clarified that the existence of non-trivial solutions depends on the algebraic properties of some related families of parameters. The problem is to find the necessary and sufficient conditions for the existence of non-trivial solutions in terms of these kinds of properties. One of the earliest results is due to Z. Daróczy [1]. It can be considered as the solution of the problem in case of n = 2. We are going to take more steps forward by solving the problem in case of n = 3.

Key words and phrases

linear functional equation spectral analysis field homomorphism 

Mathematics Subject Classification

primary 39B22 secondary 39B72 

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References

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2015

Authors and Affiliations

  1. 1.Department of Stochastics, Faculty of Natural SciencesBudapest University of Technology and Economics and MTA-BME Stochastics Research Group (04118)BudapestHungary
  2. 2.Faculty of EngineeringUniversity of DebrecenDebrecenHungary
  3. 3.Department of Geometry, Institute of Mathematics, Faculty of Science and TechnologyUniversity of DebrecenDebrecenHungary

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