Schauder and Riesz Bases for Higher-Dimensional Lebesgue Spaces Inspired by ReLU Neural Networks

Julian Billner, Cornelia Schneider

Motivated by the role of piecewise linear functions in ReLU neural networks, we study systems of dilated functions in the Lebesgue spaces $L_q([0,1{]}^d)$, $q\in (1,\infty )$. For a se…