Lipschitz and Hölder Continuity in Reproducing Kernel Hilbert Spaces

RWTH Publications (RWTH Aachen)

Abstract

Reproducing kernel Hilbert spaces (RKHSs) are very important function spaces, playing an important role in machine learning, statistics, numerical analysis and pure mathematics. Since Lipschitz and Hölder continuity are important regularity properties, with many applications in interpolation, approximation and optimization problems, in this work we investigate these continuity notion in RKHSs. We provide several sufficient conditions as well as an in depth investigation of reproducing kernels inducing prescribed Lipschitz or Hölder continuity. Apart from new results, we also collect related known results from the literature, making the present work also a convenient reference on this topic.

Authors 1

1. Christian Fiedler corresponding Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering (DSME) RWTH Aachen University