On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations
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 KL, see also G. Kiss and A. Varga KV. We are going to adopt the main theoretical tools to solve some inhomogeneous problems due to T. Szostok KKSZ08, see also KKSZ and KKSZW. They are motivated by quadrature rules of approximate integration.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.