We prove that for some parameters q ∈ (0,1) every solution f:ℝ → ℝ of the functional equation f(qx) = 1/(4q) [f(x-1) + f(x+1) + 2f(x)] which vanishes outside the interval [-q/(1-q),q/(1-q)] and is bounded in a neighbourhood of a point of that interval vanishes everywhere.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-3-1,
author = {Janusz Morawiec},
title = {On locally bounded solutions of Schilling's problem},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {169-188},
zbl = {0980.39013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-3-1}
}
Janusz Morawiec. On locally bounded solutions of Schilling's problem. Annales Polonici Mathematici, Tome 77 (2001) pp. 169-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-3-1/