Reference : On spectral synthesis in varieties containing the solutions of inhomogeneous linear f...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/31287
On spectral synthesis in varieties containing the solutions of inhomogeneous linear functional equations
English
Kiss, Gergely mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Vincze, Csaba [University of Debrecen]
2017
Aequationes Mathematicae
Springer
Yes (verified by ORBilu)
International
0001-9054
1420-8903
Basel
Switzerland
[en] Linear functional equations ; Spectral analysis ; Spectral synthesis
[en] As a continuation of our previous work [2] the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The idea is based on the fundamental work of [5]. Using spectral analysis in some related varieties we can prove the existence of special solutions (automorphisms) of the functional equation but spectral synthesis allows us to describe the entire space of solutions on a large class of finitely generated fields. It is spanned by the so-called exponential monomials which can be given in terms of automorphisms of CC and differential operators. We apply the general theory to some inhomogeneous problems motivated by quadrature rules of approximate integration [8], see also [7, 9].
Researchers
http://hdl.handle.net/10993/31287
10.1007/s00010-017-0482-y

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