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Spectrum of a homogeneous graph. (English) Zbl 1152.05348
Summary: We describe the spectrum of the Laplacian for a homogeneous graph on which a discrete group acts. This follows from a more general result which describes the spectrum of a convolution operator on a homogeneous space of a locally compact group. We also prove a version of Harnack inequality for a Schrödinger operator on an invariant homogeneous graph.
MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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