3 papers
math.AP2025
Nonlocal vector calculus on the sphere
Hadrien Montanelli, Richard Mikael Slevinsky, Qiang Du
We introduce a nonlocal vector calculus on the unit two-sphere using weakly singular integral operators. Within this framework, the operators are diagonalizable in terms of scalar…
math.NA2019
Deep ReLU networks overcome the curse of dimensionality for bandlimited functions
Hadrien Montanelli, Haizhao Yang, Qiang Du
We prove a theorem concerning the approximation of bandlimited multivariate functions by deep ReLU networks for which the curse of the dimensionality is overcome. Our theorem is ba…
math.NA2017
New error bounds for deep networks using sparse grids
Hadrien Montanelli, Qiang Du
We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks. We present new error estimates for which the curse of the dimensionality is lessene…