Thursday, May 10, 2012

1205.1944 (Daniel Lenz et al.)

Unbounded quantum graphs with unbounded boundary conditions    [PDF]

Daniel Lenz, Carsten Schubert, Ivan Veselić
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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