Whitney extension operators without loss of derivatives
[EN] For a compact set K subset of R-d we characterize the existence of a linear extension operator E: E (K) -> C-infinity(R-d) for the space of Whitney jets E (K) without loss of derivatives, that is, it satisfies the best possible continuity estimates sup{vertical bar partial derivative(alp...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/82874 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/82874 |
| Access Level: | acceso abierto |
| Palabra clave: | Whitney jets Extension operator MATEMATICA APLICADA |
| Sumario: | [EN] For a compact set K subset of R-d we characterize the existence of a linear extension operator E: E (K) -> C-infinity(R-d) for the space of Whitney jets E (K) without loss of derivatives, that is, it satisfies the best possible continuity estimates sup{vertical bar partial derivative(alpha) E(f)(x)vertical bar : vertical bar alpha vertical bar <= n, x is an element of R-d} <= C-n parallel to f parallel to(n), where parallel to . parallel to(n) denotes the n-th Whitney norm. The characterization is by a surprisingly simple purely geometric condition introduced by Jonsson, Sjogren, and Wallis: there is rho is an element of (0, 1) such that, for every x(0) is an element of K and epsilon is an element of (0, 1), there are d points x(1)..., x(d) in K n B(x(0), epsilon) satisfying dist(x(n+1), affine hull{x(0),..., x(n)}) = >= rho epsilon for all n is an element of {0,..., d - 1}. |
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