Unbounded quantum graphs with unbounded boundary conditions. Issue 8 (10th January 2014)

• Record Type: Journal Article
• Authors: Lenz, Daniel; Schubert, Carsten; Veselić, Ivan
• Is Part Of: Mathematische Nachrichten. Volume 287:Issue 8/9(2014)
• Page Start: 962
• Page End: 979
• Publication Date: 2014-01-10
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201200135
• Languages: English
• ISSNs: 0025-584X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>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.</p> </abstract>