On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations
Gergely Kiss, Csaba Vincze
TL;DR
This paper explores spectral analysis methods within specific functional spaces to solve inhomogeneous linear functional equations, extending techniques traditionally used for homogeneous equations and applying them to problems motivated by numerical integration.
Contribution
It introduces a novel application of spectral analysis to inhomogeneous functional equations in translation invariant subspaces, expanding the theoretical framework beyond homogeneous cases.
Findings
Spectral analysis effectively solves certain inhomogeneous linear functional equations.
The approach extends existing methods from homogeneous to inhomogeneous equations.
Applications include problems motivated by quadrature rules in numerical integration.
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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Taxonomy
TopicsFunctional Equations Stability Results · Diverse Scientific and Engineering Research
11footnotetext: Keywords: Linear functional equations, spectral analysis, spectral synthesis22footnotetext: MR subject classification: primary 43A45, 43A70, secondary 13F2033footnotetext: G. Kiss is supported by the Internal Research Project R-STR-1041-00-Z of the University of Luxembourgh and by the Hungarian National Foundation for Scientific Research, Grant No. K104178. Cs. Vincze is supported by the University of Debrecen’s internal research project RH/885/2013.
On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations
Gergely Kiss
Csaba Vincze