Whitney extension operators with arbitrary loss of differentiability
| Autor: | Arne Jakobs, Jochen Wengenroth, Leonhard Frerick, Enrique Jordá |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
010102 general mathematics Whitney extension operator Monotonic function 01 natural sciences 010101 applied mathematics Combinatorics symbols.namesake Operator (computer programming) Compact space Linear extension Norm (mathematics) Taylor series symbols Mityagin's problem Differentiable function 0101 mathematics MATEMATICA APLICADA Analysis Mathematics |
| Zdroj: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2020.124142 |
| Popis: | [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) with a certain loss of derivatives sigma, that is, the operator satisfies the following continuity estimates for all n is an element of N-0 and all F is an element of E(K) sup{vertical bar partial derivative(alpha) E(F)(x) : vertical bar alpha vertical bar N-0 is monotonically increasing with sigma(n) >= n and sigma(0) = 0. From our main result it follows directly that if a compact set (K) over bar admits an extension operator, then it is always possible to construct a second extension operator resembling the original Whitney operators E-n: E-n (K) -> C-n(R-d) where the evaluations of the jet occurring in the Taylor polynomials are approximated by measures. (C) 2020 Elsevier Inc. All rights reserved. 1The research of E. Jorda was partially supported by the project MTM2016-76647-P |
| Databáze: | OpenAIRE |
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