On locally bounded solutions of Schilling's problem

Volume 76 / 2001

Janusz Morawiec Annales Polonici Mathematici 76 (2001), 169-188 MSC: 39B12, 39B22. DOI: 10.4064/ap76-3-1


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.


  • Janusz MorawiecInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland

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