Timeline for On a generalization of the classical Cauchy's functional equation
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9, 2017 at 19:18 | vote | accept | Paolo Leonetti | ||
| Mar 9, 2017 at 19:17 | answer | added | Salvo Tringali | timeline score: 5 | |
| Mar 7, 2017 at 17:21 | comment | added | Salvo Tringali | I cannot edit my previous comment, but on the last line I should have written "for restricted Cauchy equations in $\mathbf R^n$" (there is nothing like "the restricted Cauchy equation"). | |
| S Mar 7, 2017 at 10:14 | history | suggested | Amir Sagiv | CC BY-SA 3.0 |
latex edits + english
|
| Mar 7, 2017 at 10:12 | comment | added | Jules Lamers | For $f$ a map between complex vector spaces the "multidimensional Cauchy equation" is also a special case of Thm 7.2 in Risteski and Covachev's Complex vector functional equations (2002). For more about the solution to the Cauchy matrix functional equation they refer to Gheorghiu, C. R. Acad. Sci. Paris 256, 3562 (1963) and Kuwagaki, J Math Soc Japan 14, 359 (1962). | |
| Mar 7, 2017 at 10:00 | review | Suggested edits | |||
| S Mar 7, 2017 at 10:14 | |||||
| Mar 7, 2017 at 9:18 | comment | added | Salvo Tringali | You may want to mention that a solution to the "multidimensional Cauchy equation" is known for the general case of a continuous additive function $f: \mathbf R^n \to \mathbf R$ (Theorem 5.5.2 in the 2nd edition of M. Kuczma's An Introduction to the Theory of Functional Equations and Inequalities), and that much is also known for the restricted Cauchy equation in $\mathbf R^n$ (Section 13.6 in Kuczma's book). | |
| Mar 7, 2017 at 9:05 | history | asked | Paolo Leonetti | CC BY-SA 3.0 |