Annales Henri Poincaré

, Volume 15, Issue 9, pp 1697–1732 | Cite as

Pseudo-Differential Calculus on Homogeneous Trees

  • Etienne Le Masson


To study concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct in this paper a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol classes and associated operators. We prove that these operators are bounded on L 2 and give adjoint and product formulas. Finally, we compute the symbol of the commutator of a pseudo-differential operator with the Laplacian.


Regular Graph Symmetry Condition Rapid Decay Homogeneous Tree Hyperbolic Surface 
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© Springer Basel 2013

Authors and Affiliations

  1. 1.Université Paris-Sud 11Orsay CedexFrance

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