Constructs symmetric analytic positivity-preserving Ornstein-Uhlenbeck semigroups on rooted metric trees with Gaussian measures, establishes compactness and eigenvalue asymptotics, and reduces regular cases to half-line problems via adapted Naimark-Solomyak decomposition.
Kurasov,Spectral Geometry of Graphs, Operator Theory: Advances and Applications, Springer, Cham (2024), 10.1007/978-3-662-67872-5
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Quantum graphs are presented as a paradigmatic model for quantum chaos, with the paper providing a didactical overview of foundational results and some recent developments.
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Ornstein--Uhlenbeck semigroup on rooted trees
Constructs symmetric analytic positivity-preserving Ornstein-Uhlenbeck semigroups on rooted metric trees with Gaussian measures, establishes compactness and eigenvalue asymptotics, and reduces regular cases to half-line problems via adapted Naimark-Solomyak decomposition.
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Quantum graph models of quantum chaos: an introduction and some recent applications
Quantum graphs are presented as a paradigmatic model for quantum chaos, with the paper providing a didactical overview of foundational results and some recent developments.