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Schauder and Riesz Bases for Higher-Dimensional Lebesgue Spaces Inspired by ReLU Neural Networks
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 sequence $τ\in\ell_1$ we consider the operator $T_τg(x)=\sum_{k=1}^\infty τ_k g(kx)$ and the function system $\mathcal Z^τ
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