Contraction semigroups on metric graphs
Vadim Kostrykin, Jurgen Potthoff, Robert Schrader
TL;DR
This paper investigates contraction semigroups generated by Laplace operators on metric graphs, focusing on their continuity, positivity preservation, and characterization of Feller semigroup generators, extending understanding beyond self-adjoint cases.
Contribution
It provides new criteria for contraction semigroups on metric graphs and characterizes generators of Feller semigroups, including non-self-adjoint cases.
Findings
Criteria for continuity and positivity preservation of semigroups
Characterization of generators of Feller semigroups on metric graphs
Extension to non-self-adjoint Laplace operators
Abstract
The main objective of the present work is to study contraction semigroups generated by Laplace operators on metric graphs, which are not necessarily self-adjoint. We prove criteria for such semigroups to be continuity and positivity preserving. Also we provide a characterization of generators of Feller semigroups on metric graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Fixed Point Theorems Analysis · Limits and Structures in Graph Theory