Some remarks on the Krein--von Neumann extension of different Laplacians

Delio Mugnolo

Published 2014-02-26Version 1

We discuss the Krein--von Neumann extensions of three Laplacian-type operators -- on discrete graphs, quantum graphs, and domains. In passing we present a class of one-dimensional elliptic operators such that for any $n\in \mathbb N$ infinitely many elements of the class have $n$-dimensional null space.