Abstract
Fix , and assume that, for every , the functions and are Lebesgue-measurable, is almost everywhere approximately differentiable with for almost all , there exists such that the set is of Lebesgue measure zero, satisfy Luzin’s condition N, and the set is of Lebesgue measure zero for every set of Lebesgue measure zero. We show that the formula defines a linear and continuous operator , and then we obtain results on the existence and uniqueness of solutions of the equation with a given .
Citation
Janusz Morawiec. Thomas Zürcher. "Some classes of linear operators involved in functional equations." Ann. Funct. Anal. 10 (3) 381 - 394, August 2019. https://doi.org/10.1215/20088752-2018-0037
Information