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arXiv · 1205.1944

Unbounded quantum graphs with unbounded boundary conditions

Daniel Lenz·Carsten Schubert·Ivan Veselić
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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.

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Daniel Lenz, Carsten Schubert, Ivan Veselić. 2012-05-09. Unbounded quantum graphs with unbounded boundary conditions. https://doi.org/10.1002/mana.201200135

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