The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees
G. Palmirotta, Y. Sire, J.-P. Anker, Journal of Differential Equations (2026).
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Palmirotta, GuendalinaLibreCat;
Sire, Yannick;
Anker, Jean-Philippe
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We investigate dispersive and Strichartz estimates for the Schrödinger 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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Journal of Differential Equations
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Palmirotta G, Sire Y, Anker J-P. The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. Journal of Differential Equations. Published online 2026. doi:10.1016/j.jde.2025.114065
Palmirotta, G., Sire, Y., & Anker, J.-P. (2026). The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. Journal of Differential Equations. https://doi.org/10.1016/j.jde.2025.114065
@article{Palmirotta_Sire_Anker_2026, title={The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees}, DOI={10.1016/j.jde.2025.114065}, journal={Journal of Differential Equations}, publisher={Elsevier}, author={Palmirotta, Guendalina and Sire, Yannick and Anker, Jean-Philippe}, year={2026} }
Palmirotta, Guendalina, Yannick Sire, and Jean-Philippe Anker. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” Journal of Differential Equations, 2026. https://doi.org/10.1016/j.jde.2025.114065.
G. Palmirotta, Y. Sire, and J.-P. Anker, “The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees,” Journal of Differential Equations, 2026, doi: 10.1016/j.jde.2025.114065.
Palmirotta, Guendalina, et al. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” Journal of Differential Equations, Elsevier, 2026, doi:10.1016/j.jde.2025.114065.
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