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math.FA2026
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 , . For a se…
math.AP2026
Fractional gradients and nonlocal PDEs in variable exponent spaces
Susana Moura, Cornelia Schneider
We develop a theory of distributional Riesz fractional gradients in variable exponent Lebesgue spaces and introduce the associated nonlocal Sobolev spaces. Moreover, Sobolev, Hardy…