The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees
G. Palmirotta, Y. Sire, J.-P. Anker, ArXiv:2412.00780 (2024).
Download
No fulltext has been uploaded.
Preprint
| English
Author
Palmirotta, GuendalinaLibreCat;
Sire, Yannick;
Anker, Jean-Philippe
Department
Project
Abstract
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.
Publishing Year
Journal Title
arXiv:2412.00780
LibreCat-ID
Cite this
Palmirotta G, Sire Y, Anker J-P. The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. arXiv:241200780. Published online 2024.
Palmirotta, G., Sire, Y., & Anker, J.-P. (2024). The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. In arXiv:2412.00780.
@article{Palmirotta_Sire_Anker_2024, title={The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees}, journal={arXiv:2412.00780}, author={Palmirotta, Guendalina and Sire, Yannick and Anker, Jean-Philippe}, year={2024} }
Palmirotta, Guendalina, Yannick Sire, and Jean-Philippe Anker. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” ArXiv:2412.00780, 2024.
G. Palmirotta, Y. Sire, and J.-P. Anker, “The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees,” arXiv:2412.00780. 2024.
Palmirotta, Guendalina, et al. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” ArXiv:2412.00780, 2024.
arXiv 
Google Scholar