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Aequationes mathematicae

, Volume 91, Issue 4, pp 663–690 | Cite as

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

  • Gergely KissEmail author
  • Csaba Vincze
Article

Abstract

The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations 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 the case of homogeneous linear functional equations. The foundations of the theory can be found in Kiss and Varga (Aequat Math 88(1):151–162, 2014) and Kiss and Laczkovich (Aequat Math 89(2):301–328, 2015). We are going to adopt the main theoretical tools to solve some inhomogeneous problems due to Koclȩga-Kulpa and Szostok (Ann Math Sylesianae 22:27–40, 2008), see also Koclȩga-Kulpa and Szostok (Georgian Math J 16:725–736, 2009; Acta Math Hung 130(4):340–348, 2011). They are motivated by quadrature rules of approximate integration.

Keywords

Linear functional equations Spectral analysis Spectral synthesis 

Mathematics Subject Classification

Primary 43A45 43A70 Secondary 13F20 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Mathematics Research Unit, FSTCUniversity of LuxembourgLuxembourgLuxembourg
  2. 2.Department of Geometry, Institute of Mathematics, Faculty of Science and TechnologyUniversity of DebrecenDebrecenHungary

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