Beschreibung:
<jats:p>All functions mentioned in this paper will be real-valued. If <jats:italic>f</jats:italic><jats:sub>1</jats:sub>, <jats:italic>f</jats:italic><jats:sub>2</jats:sub>, <jats:italic>g</jats:italic> are nonnegative functions on a set <jats:italic>S</jats:italic> that satisfy g ≦ <jats:italic>f</jats:italic><jats:sub>1</jats:sub> + <jats:italic>f</jats:italic><jats:sub>2</jats:sub>, the <jats:italic>Riesz decomposition problem</jats:italic> associated with these data is to find functions <jats:italic>g<jats:sub>i</jats:sub></jats:italic> on <jats:italic>S</jats:italic> such that</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" orientation="portrait" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0008414X00049245_eqn01" /></jats:disp-formula></jats:p><jats:p>The formula</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" orientation="portrait" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0008414X00049245_eqn02" /></jats:disp-formula></jats:p><jats:p>always furnishes a solution. The problem becomes more interesting if one asks under what conditions one can find solutions that are, roughly speaking, as smooth as the data.</jats:p>