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

Abstract

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.

13 pages

References in corpus (3)

• Variational and Semigroup Methods for Waves and Diffusion in Networks
• On moments-preserving cosine families and semigroups in $C[0,1]$
• Markovian Extensions of Symmetric Second Order Elliptic Differential Operators

Cited by in corpus (1)

• Bi-Laplacians on graphs and networks