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math.FA2025
Bases of Lebesgue spaces formed by neural networks
Vladimir Kulbatov, Jan Lang, Cornelia Schneider +1
The seminal work of Daubechies, DeVore, Foucart, Hanin, and Petrova introduced in 2022 a sequence of univariate piece-wise linear functions, which resemble the classical Fourier ba…
math.FA2025
Non-strict singularity of optimal Sobolev embeddings
Jan Lang, Zdeněk Mihula
We investigate the operator-theoretic property of strict singularity for optimal Sobolev embeddings within the general framework of rearrangement-invariant function spaces (r.i. sp…
math.FA2025★ 1 cited
A Bourgain-Gromov problem on non-compact Sobolev-Lorentz embeddings
Chian Yeong Chuah, Jan Lang, Liding Yao
We study the non-compact Sobolev embeddings into the optimal scale of Lorentz spaces, , where , $1 \le m \l…