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

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 $n\in \mathbb N$infinitelymanyelementsoftheclasshave$n$-dimensional null space.