5 papers
The next Fourier transform: rewiring, representation, and artificial mathematical creativity
Luca Fanelli
What distinguishes the solution of a difficult mathematical problem from a conceptual revolution? Some mathematical innovations do more than establish new results: they reorganize…
Bootstrap Diagnostic Tests
Giuseppe Cavaliere, Luca Fanelli, Iliyan Georgiev
Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violati…
Intertwining operators beyond the Stark Effect
Luca Fanelli, Xiaoyan Su, Ying Wang +2
The main mathematical manifestation of the Stark effect in quantum mechanics is the shift and the formation of clusters of eigenvalues when a spherical Hamiltonian is perturbed by…
Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
Miguel Á. Alejo, Lucrezia Cossetti, Luca Fanelli +2
We consider the subcritical nonlinear Schrödinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximat…
Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials
Lucrezia Cossetti, Luca Fanelli, David Krejcirik
We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under whi…