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math.FA2025
Saturation theorems for neural network operators by solving elliptic and hyperbolic PDEs with analytical and semi-analytical inverse problems
Danilo Costarelli
This paper addresses inverse problems (in a broad sense) for two classes of multivariate neural network (NN) operators, with particular emphasis on saturation results, and both ana…
math.FA2025
Modular convergence of Steklov sampling operators in Orlicz spaces
Danilo Costarelli, Erika Russo
In this paper, we deal with the family of Steklov sampling operators in the general setting of Orlicz spaces. The main result of the paper is a modular convergence theorem establis…
math.FA2025★ 2 cited
Strong and weak sharp bounds for Neural Network Operators in Sobolev-Orlicz spaces and their quantitative extensions to Orlicz spaces
Danilo Costarelli, Michele Piconi
In this paper, we establish sharp bounds for a family of Kantorovich-type neural network operators within the general frameworks of Sobolev-Orlicz and Orlicz spaces. We establish b…