d'Alembert's other functional equation on monoids with an involution
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| 024 | 7 | 0 | |a 10.1007/s00010-014-0303-5 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0303-5 | ||
| 245 | 0 | 0 | |a d'Alembert's other functional equation on monoids with an involution |h [Elektronische Daten] |c [Bruce Ebanks, Henrik Stetkær] |
| 520 | 3 | |a This paper treats a functional equation of d'Alembert, namely f(x + y) − f(x − y) =g(x)h(y), in the setting of groups and monoids that need not be abelian. Of the several possibilities for generalizing x − y to the non-abelian case, here we replace it by σ(y)x where σ is an involutive automorphism, and find the complex-valued solutions (f, g, h) of f(xy) − f(σ(y)x) =g(x)h(y) in terms of multiplicative and additive functions. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a d'Alembert |2 nationallicence | |
| 690 | 7 | |a involutive automorphism |2 nationallicence | |
| 690 | 7 | |a functional equation |2 nationallicence | |
| 690 | 7 | |a non-abelian |2 nationallicence | |
| 690 | 7 | |a monoid |2 nationallicence | |
| 700 | 1 | |a Ebanks |D Bruce |u Mississippi State University, Mississippi State, USA |4 aut | |
| 700 | 1 | |a Stetkær |D Henrik |u Aarhus University, Aarhus, Denmark |4 aut | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 187-206 |x 0001-9054 |q 89:1<187 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0303-5 |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/s00010-014-0303-5 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ebanks |D Bruce |u Mississippi State University, Mississippi State, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Stetkær |D Henrik |u Aarhus University, Aarhus, Denmark |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 187-206 |x 0001-9054 |q 89:1<187 |1 2015 |2 89 |o 10 | ||