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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Estimates for functions of the Laplace operator on homogeneous trees


Authors: Michael Cowling, Stefano Meda and Alberto G. Setti
Journal: Trans. Amer. Math. Soc. 352 (2000), 4271-4293
MSC (1991): Primary 43A85; Secondary 20E08, 43A90, 22E35
Published electronically: April 14, 2000
MathSciNet review: 1653343
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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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Additional Information

Michael Cowling
Affiliation: School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia
Email: m.cowling@unsw.edu.au

Stefano Meda
Affiliation: Dipartimento di Matematica, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy
Address at time of publication: Department of Statistics, University of Milan-Bicocca, Edificio U7 II piano, v. Le Sarca 202, I-20100 Milan, Italy
Email: stemed@ipmma1.mate.polimi.it

Alberto G. Setti
Affiliation: Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italy
Address at time of publication: Faculty of Science, Universitá dell’Insubria-1 Como via Lucini 3, I-22100 Como, Italy
Email: setti@fis.unico.it

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02460-0
PII: S 0002-9947(00)02460-0
Keywords: Homogeneous trees, Laplace--Beltrami operator, spherical functions, harmonic analysis
Received by editor(s): October 4, 1996
Published electronically: April 14, 2000
Additional Notes: Work partially supported by the Australian Research Council and the Italian M.U.R.S.T
Article copyright: © Copyright 2000 American Mathematical Society