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- W4300874451 abstract "We study Laplacians associated to a graph and single out a class of such operators with special regularity properties. In the case of locally finite graphs, this class consists of all selfadjoint, non-negative restrictions of the standard formal Laplacian and we can characterize the Dirichlet and Neumann Laplacians as the largest and smallest Markovian restrictions of the standard formal Laplacian. In the case of general graphs, this class contains the Dirichlet and Neumann Laplacians and we describe how these may differ from each other, characterize when they agree, and study connections to essential selfadjointness and stochastic completeness. Finally, we study basic common features of all Laplacians associated to a graph. In particular, we characterize when the associated semigroup is positivity improving and present some basic estimates on its long term behavior. We also discuss some situations in which the Laplacian associated to a graph is unique and, in this context, characterize its boundedness." @default.
- W4300874451 created "2022-10-04" @default.
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- W4300874451 date "2011-03-18" @default.
- W4300874451 modified "2023-09-25" @default.
- W4300874451 title "Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions" @default.
- W4300874451 doi "https://doi.org/10.48550/arxiv.1103.3695" @default.
- W4300874451 hasPublicationYear "2011" @default.
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