Pointwise convergence to the initial data for nonlocal dyadic diffusions
In this paper we solve the initial value problem for the diffusion induced by dyadic fractional derivative s in R +. First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show tha...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/30630 |
| Acceso en línea: | http://hdl.handle.net/11336/30630 |
| Access Level: | acceso abierto |
| Palabra clave: | pointwise convergence nonlocal diffusion dyadic fractional derivatives Haar bases https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper we solve the initial value problem for the diffusion induced by dyadic fractional derivative s in R +. First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show that this kernel admits an integrable and decreasing majorant that involves the dyadic distance. This allows us to provide an estimate of the maximal operator of the diffusion by the Hardy-Littlewood dyadic maximal operator. As a consequence we obtain the pointwise convergence to the initial data. |
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