On locally bounded solutions of Schilling's problem
Volume 76 / 2001
Annales Polonici Mathematici 76 (2001), 169-188
MSC: 39B12, 39B22.
DOI: 10.4064/ap76-3-1
Abstract
We prove that for some parameters $q\in (0,1)$ every solution $f:{\mathbb R}\rightarrow {\mathbb R}$ of the functional equation $$ f(qx)={1\over 4q}[f(x-1)+f(x+1)+2f(x)] $$ 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.
