Unbounded quantum graphs with unbounded boundary conditions

Abstract

We consider metric graphs with a uniform lower bound on the edge lengths but no further restrictions. We discuss how to describe every local self-adjoint Laplace operator on such graphs by boundary conditions in the vertices given by projections and self-adjoint operators. We then characterize the lower bounded self-adjoint Laplacians and determine their associated quadratic form in terms of the operator families encoding the boundary conditions.

References in corpus (1)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators

Cited by in corpus (5)

• Spectral Theory of Infinite Quantum Graphs
• Spectral enclosures for non-self-adjoint extensions of symmetric operators
• New relations between discrete and continuous transition operators on (metric) graphs
• Embedded trace operator for infinite metric trees
• Dissipative extensions and port-Hamiltonian operators on networks