In this paper we consider the Aleksandrov equation f(L + x) = f(L) + f(x) where L is contained in Rn and f: L --> R and we describe the class of solutions bounded from below, with zeros and assuming on the boundary of the set of zeros only values multiple of a fixed a > 0. This class is the natural generalization of that described by Aleksandrov itself in the one-dimensional case.
@article{urn:eudml:doc:39278,
title = {Una classe di soluzioni con zeri dell'equazione funzionale di Aleksandrov.},
journal = {Stochastica},
volume = {13},
year = {1992},
pages = {23-30},
zbl = {0770.39005},
mrnumber = {MR1197324},
language = {it},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39278}
}
Borelli Forti, Constanza. Una classe di soluzioni con zeri dell'equazione funzionale di Aleksandrov.. Stochastica, Tome 13 (1992) pp. 23-30. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39278/