caa a22 4500 60550802X CHVBK 20210128100634.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00010-014-0314-2 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0314-2 Schwaiger Jens Institut für Mathematik und Wiss. Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010, Graz, Austria aut On the construction of functional equations with prescribed general solution [Elektronische Daten] [Jens Schwaiger] Given rational vector spaces V, W a mapping $${f \colon V \to W}$$ f : V → W is called a generalized polynomial of degree at most n, if there are homogeneous generalized polynomials f i of degree i such that $${f = \sum_{i = 0}^n f_i}$$ f = ∑ i = 0 n f i . Homogeneous generalized polynomials f i of degree i are mappings of the form $${f_i (x) = f_i^*(x, x, \ldots , x)}$$ f i ( x ) = f i ∗ ( x , x , ... , x ) with $${f_i^* \colon V^i \to W i}$$ f i ∗ : V i → W i -linear. In the literature one may find quite a lot of functional equations such that their general solution is of the form f n or $${f_n + f_{n - 1}}$$ f n + f n - 1 where n is a small positive integer (≤ 6 or ≤ 4 respectively). In this paper, given an arbitrary positive integer n and an arbitrary subset $${L \subseteq \{0, 1, \ldots, n\}}$$ L ⊆ { 0 , 1 , ... , n } such that $${n \in L}$$ n ∈ L , a method is described to find (many) functional equations, such that their general solution is given by $${\sum_{i \in L} f_i}$$ ∑ i ∈ L f i . For the cases $${L = \{n\}}$$ L = { n } and $${L = \{n - 1, n\}}$$ L = { n - 1 , n } additional equations are given. Springer Basel, 2014 Functional equations with prescribed general solution nationallicence generalized polynomials nationallicence Aequationes mathematicae Springer Basel 89/1(2015-02-01), 23-40 0001-9054 89:1<23 2015 89 10 https://doi.org/10.1007/s00010-014-0314-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0314-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Schwaiger Jens Institut für Mathematik und Wiss. Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010, Graz, Austria aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/1(2015-02-01), 23-40 0001-9054 89:1<23 2015 89 10