Estimates for functions of the Laplace operator on homogeneous trees

Cowling, Michael; Meda, Stefano; Setti, Alberto

doi:10.1090/S0002-9947-00-02460-0

Estimates for functions of the Laplace operator on homogeneous trees
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by Michael Cowling, Stefano Meda and Alberto G. Setti PDF

Trans. Amer. Math. Soc. 352 (2000), 4271-4293 Request permission

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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