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The Schr\"odinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees

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arxiv 2412.00780 v1 pith:GSRSHJWF submitted 2024-12-01 math.AP

Jean-Philippe Anker , Guendalina Palmirotta , Yannick Sire This is my paper · ORCID
classification math.AP
keywords spacesestimatesfractionalhomogeneoushyperboliclaplaciantreesequation
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We investigate dispersive and Strichartz estimates for the Schr\"odinger equation involving the fractional Laplacian in real hyperbolic spaces and their discrete analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz estimates on Euclidean spaces for the fractional Laplacian exhibit loss of derivatives. A similar phenomenon appears on real hyperbolic spaces. However, such a loss disappears on homogeneous trees, due to the triviality of the estimates for small times.

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  1. The Logarithmic Laplacian on General Graphs

    math.AP 2025-07 conditional novelty 6.0 of 10

    The logarithmic Laplacian on weighted graphs is defined via a Bochner integral, given a kernel formula under stochastic completeness, and shown on Z^d to have sharp kernel bounds and exact diffusion asymptotics.

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