Uniform convergence of Nyström discretization on Hölder spaces

Abstract

We establish that Nyström discretizations of linear Fredholm integral operators on Hölder spaces converge in the operator norm while preserving the consistency order of the quadrature or cubature rule. This allows to employ tools from classical perturbation theory, rather than collective compactness, when studying numerical approximations of integral operators, as well as applications in for instance the field of nonautonomous dynamical systems.