{"user_id":"109467","_id":"57580","year":"2024","type":"preprint","date_created":"2024-12-04T16:21:38Z","title":"The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees","citation":{"ieee":"G. Palmirotta, Y. Sire, and J.-P. Anker, “The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees,” <i>arXiv:2412.00780</i>. 2024.","ama":"Palmirotta G, Sire Y, Anker J-P. The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. <i>arXiv:241200780</i>. Published online 2024.","short":"G. Palmirotta, Y. Sire, J.-P. Anker, ArXiv:2412.00780 (2024).","mla":"Palmirotta, Guendalina, et al. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” <i>ArXiv:2412.00780</i>, 2024.","bibtex":"@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} }","chicago":"Palmirotta, Guendalina, Yannick Sire, and Jean-Philippe Anker. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” <i>ArXiv:2412.00780</i>, 2024.","apa":"Palmirotta, G., Sire, Y., &#38; Anker, J.-P. (2024). The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. In <i>arXiv:2412.00780</i>."},"author":[{"first_name":"Guendalina","last_name":"Palmirotta","full_name":"Palmirotta, Guendalina","id":"109467"},{"first_name":"Yannick","last_name":"Sire","full_name":"Sire, Yannick"},{"full_name":"Anker, Jean-Philippe","last_name":"Anker","first_name":"Jean-Philippe"}],"department":[{"_id":"10"},{"_id":"548"}],"external_id":{"arxiv":["2412.00780"]},"status":"public","project":[{"grant_number":"491392403","_id":"356","name":"TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem Volumen (Teilprojekt B02)"}],"publication":"arXiv:2412.00780","abstract":[{"text":"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.","lang":"eng"}],"language":[{"iso":"eng"}],"date_updated":"2024-12-04T16:34:09Z"}