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New Relations Between Discrete and Continuous Transition Operators on (Metric) Graphs

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Abstract

We establish several new relations between the discrete transition operator, the continuous Laplacian and the averaging operator associated with combinatorial and metric graphs. It is shown that these operators can be expressed through each other in a very explicit way. In particular, the averaging operator appears to be closely related to the solutions of the associated wave equation. The machinery used allows one to study a class of infinite graphs without assumption on the local finiteness.

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Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany

    Daniel Lenz

  2. Laboratoire de mathématiques (UMR 8628 du CNRS), Université Paris-Sud, Bâtiment 425, 91405, Orsay Cedex, France

    Konstantin Pankrashkin

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Lenz, D., Pankrashkin, K. New Relations Between Discrete and Continuous Transition Operators on (Metric) Graphs. Integr. Equ. Oper. Theory 84, 151–181 (2016). https://doi.org/10.1007/s00020-015-2253-2

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  • DOI: https://doi.org/10.1007/s00020-015-2253-2

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