Daniel Lenz, Carsten Schubert, Ivan Veselić: Unbounded quantum graphs with unbounded boundary conditions

Author(s):

Daniel Lenz
Carsten Schubert
Ivan Veselić

Title:

Daniel Lenz, Carsten Schubert, Ivan Veselić: Unbounded quantum graphs with unbounded boundary conditions

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 10, 2013

Mathematics Subject Classification:

47B25	[]
35J05	[]
81Q35	[]

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.

Keywords:

Language:

English

Publication time:

06/2013