Tangent measures and Lp estimation of tangent maps
We analyze under what conditions the best Lp- linear fittings of the action of a mapping on small balls give reliable estimates of the tangent map Df. We show that there is an inverse relationslúp between the conditions on the regularity, in terms of local densities, of the underlying measure and th...
| Autores: | , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 1996 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/64116 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/64116 |
| Access Level: | acceso abierto |
| Palabra clave: | Lp- estimation Tangent maps Hausdorff measures Tangent measures Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| Sumario: | We analyze under what conditions the best Lp- linear fittings of the action of a mapping on small balls give reliable estimates of the tangent map Df. We show that there is an inverse relationslúp between the conditions on the regularity, in terms of local densities, of the underlying measure and the smoothness of the mapping f which are required to ensure the goodness of the estimates. The above results can be applied to the estimation of tangent maps in two empirical settings: from fiuite samples of a given probability distribution on mn and from fiuite orbits of smooth dynamical systems. |
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