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dc.contributor.author | Frerick, Leonhard![]() |
es_ES |
dc.contributor.author | Arne Jakobs![]() |
es_ES |
dc.contributor.author | Jorda Mora, Enrique![]() |
es_ES |
dc.contributor.author | Wengenroth, Jochen![]() |
es_ES |
dc.date.accessioned | 2021-07-21T03:31:25Z | |
dc.date.available | 2021-07-21T03:31:25Z | |
dc.date.issued | 2020-09-01 | es_ES |
dc.identifier.issn | 0022-247X | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/169644 | |
dc.description.abstract | [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, x is an element of R-d vertical bar} <= C-n parallel to F parallel to(sigma(n)), where parallel to.parallel to(sigma(n)) denotes the Whitney norm and the map s: N-0 -> 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. | es_ES |
dc.description.sponsorship | 1The research of E. Jorda was partially supported by the project MTM2016-76647-P | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Elsevier | es_ES |
dc.relation.ispartof | Journal of Mathematical Analysis and Applications | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.subject | Whitney extension operator | es_ES |
dc.subject | Mityagin's problem | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | Whitney extension operators with arbitrary loss of differentiability | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1016/j.jmaa.2020.124142 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2016-76647-P/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada | es_ES |
dc.description.bibliographicCitation | Frerick, L.; Arne Jakobs; Jorda Mora, E.; Wengenroth, J. (2020). Whitney extension operators with arbitrary loss of differentiability. Journal of Mathematical Analysis and Applications. 489(1):1-13. https://doi.org/10.1016/j.jmaa.2020.124142 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.1016/j.jmaa.2020.124142 | es_ES |
dc.description.upvformatpinicio | 1 | es_ES |
dc.description.upvformatpfin | 13 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 489 | es_ES |
dc.description.issue | 1 | es_ES |
dc.relation.pasarela | S\420207 | es_ES |
dc.contributor.funder | Ministerio de Economía y Competitividad | es_ES |
dc.description.references | Frerick, L., Jordá, E., & Wengenroth, J. (2011). Tame linear extension operators for smooth Whitney functions. Journal of Functional Analysis, 261(3), 591-603. doi:10.1016/j.jfa.2011.04.008 | es_ES |
dc.description.references | Frerick, L., Jordá, E., & Wengenroth, J. (2016). Whitney extension operators without loss of derivatives. Revista Matemática Iberoamericana, 32(2), 377-390. doi:10.4171/rmi/888 | es_ES |
dc.description.references | Goncharov, A. (1996). A compact set without Markov’s property but with an extension operator for $C^∞$-functions. Studia Mathematica, 119(1), 27-35. doi:10.4064/sm-119-1-27-35 | es_ES |
dc.description.references | Goncharov, A., & Ural, Z. (2017). Mityagin’s extension problem. Progress report. Journal of Mathematical Analysis and Applications, 448(1), 357-375. doi:10.1016/j.jmaa.2016.11.001 | es_ES |
dc.description.references | Whitney, H. (1934). Analytic extensions of differentiable functions defined in closed sets. Transactions of the American Mathematical Society, 36(1), 63-63. doi:10.1090/s0002-9947-1934-1501735-3 | es_ES |
dc.description.references | Tidten, M. (1979). Fortsetzungen von C?-Funktionen, welche auf einer abgeschlossenen Menge in ?n definiert sind. Manuscripta Mathematica, 27(3), 291-312. doi:10.1007/bf01309013 | es_ES |