On the construction of functional equations with prescribed general solution
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| 008 | 210128e20150201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0314-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0314-2 | ||
| 100 | 1 | |a Schwaiger |D Jens |u Institut für Mathematik und Wiss. Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010, Graz, Austria |4 aut | |
| 245 | 1 | 0 | |a On the construction of functional equations with prescribed general solution |h [Elektronische Daten] |c [Jens Schwaiger] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Functional equations with prescribed general solution |2 nationallicence | |
| 690 | 7 | |a generalized polynomials |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 23-40 |x 0001-9054 |q 89:1<23 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0314-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0314-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Schwaiger |D Jens |u Institut für Mathematik und Wiss. Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010, Graz, Austria |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 23-40 |x 0001-9054 |q 89:1<23 |1 2015 |2 89 |o 10 | ||