Mityagin's extension problem. Progress report
| Autor: | Alexander Goncharov, Zeliha Ural |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
010103 numerical & computational mathematics
Characterization (mathematics) Space (mathematics) 01 natural sciences Operator (computer programming) 46E10 31A15 41A10 Classical Analysis and ODEs (math.CA) FOS: Mathematics 0101 mathematics Mathematics Discrete mathematics Markov chain Applied Mathematics 010102 general mathematics Hausdorff space Whitney functions Extension (predicate logic) Extension problem Hausdorff measures Functional Analysis (math.FA) Mathematics - Functional Analysis Compact space Mathematics - Classical Analysis and ODEs Continuous linear extension Markov's factors Analysis |
| Zdroj: | Journal of Mathematical Analysis and Applications |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2016.11.001 |
| Popis: | Given a compact set K subset of R-d, let epsilon(K) denote the space of Whitney jets on K. The compact set K is said to have the extension property if there exists a continuous linear extension operator W : epsilon(K) -> C infinity (R-d). In 1961 B.S. Mityagin posed a problem to give a characterization of the extension property in geometric terms. We show that there is no such complete description in terms of densities of Hausdorff contents or related characteristics. Also the extension property cannot be characterized in terms of growth of Markov's factors for the set. (C) 2016 Elsevier Inc. All rights reserved. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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