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arXiv · 1704.04753

On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations

Gergely Kiss·Csaba Vincze
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Abstract

The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The application of spectral analysis in some related varieties is a new and important trend in the theory of functional equations; especially they have successful applications in case of homogeneous linear functional equations. The foundation of the theory can be found in M. Laczkovich and G. Kiss \cite{KL}, see also G. Kiss and A. Varga \cite{KV}. We are going to adopt the main theoretical tools to solve some inhomogeneous problems due to T. Szostok \cite{KKSZ08}, see also \cite{KKSZ} and \cite{KKSZW}. They are motivated by quadrature rules of approximate integration.

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Gergely Kiss, Csaba Vincze. 2017-04-16. On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations. https://arxiv.org/abs/1704.04753

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