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An Isaac Newton Institute Workshop

Quantum Graphs, their Spectra and Applications

Contractive semigroups on metric graphs

Author: V. Kostrykin (Aachen/Clausthal)

Abstract

The talk is devoted to the study of general (not necessarily self-adjoint) Laplace operators on metric graphs generating contractive semigroups. We present necessary and sufficient conditions on the boundary conditions at the vertices of the graph, ensuring the contractivity of generated semigroups. Preservation of continuity and positivity under such semigroups will also be discussed. The talk is based on a joint work with J.~Potthoff and R.~Schrader.