In this paper, we study the heat equation on a homogeneous graph, relative to the natural (nearest-neighbour) Laplacian. We find pointwise estimates for the heat and resolvent kernels, and the L-p-L-q mapping properties of the corresponding operators
Cowling, M., Meda, S., Setti, A. (2000). Estimates for functions of the Laplace operator on homogeneous trees. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 352(9), 4271-4293 [10.1090/S0002-9947-00-02460-0].
Estimates for functions of the Laplace operator on homogeneous trees
Meda, S;
2000
Abstract
In this paper, we study the heat equation on a homogeneous graph, relative to the natural (nearest-neighbour) Laplacian. We find pointwise estimates for the heat and resolvent kernels, and the L-p-L-q mapping properties of the corresponding operators
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