Published online by Cambridge University Press: 20 November 2018
All functions mentioned in this paper will be real-valued. If f1, f2, g are nonnegative functions on a set S that satisfy g ≦ f1 + f2, the Riesz decomposition problem associated with these data is to find functions gi on S such that
The formula
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.