An Uncertainty Principle for Solutions of the Schrödinger Equation on H-Type Groups
In this paper we consider uncertainty principles for solutions of certain partial differential equations on H -type groups. We first prove that, on H -type groups, the heat kernel is an average of Gaussians in the central variable, so that it does not satisfy a certain reformulation of Hardy’s uncer...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/52480 |
| Acceso en línea: | http://hdl.handle.net/10810/52480 |
| Access Level: | acceso abierto |
| Palabra clave: | uncertainty principle H-type group Schrödinger equation heat kernel |
| Sumario: | In this paper we consider uncertainty principles for solutions of certain partial differential equations on H -type groups. We first prove that, on H -type groups, the heat kernel is an average of Gaussians in the central variable, so that it does not satisfy a certain reformulation of Hardy’s uncertainty principle. We then prove the analogue of Hardy’s uncertainty principle for solutions of the Schrödinger equation with potential on H -type groups. This extends the free case considered by Ben Saïd et al. [‘Uniqueness of solutions to Schrödinger equations on H-type groups’, J. Aust. Math. Soc. (3) 95 (2013), 297–314] and by Ludwig and Müller [‘Uniqueness of solutions to Schrödinger equations on 2-step nilpotent Lie groups’, Proc. Amer. Math. Soc. 142 (2014), 2101–2118]. |
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