Pseudo-differential calculus on homogeneous trees

Etienne Le Masson

doi:10.1007/s00023-013-0284-2

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arXiv · 1302.5387

Pseudo-differential calculus on homogeneous trees

Etienne Le Masson

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Abstract

In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct 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.

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BibTeX RIS

Etienne Le Masson. 2013-02-21. Pseudo-differential calculus on homogeneous trees. https://doi.org/10.1007/s00023-013-0284-2

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