On C1 Whitney extension theorem in Banach spaces
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10511068" target="_blank" >RIV/00216208:11320/25:10511068 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YUnOtemcqu" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=YUnOtemcqu</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2025.111061" target="_blank" >10.1016/j.jfa.2025.111061</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
On C1 Whitney extension theorem in Banach spaces
Popis výsledku v původním jazyce
Our note is a complement to recent articles [17] (2011) and [18] (2013) by M. Jim & eacute;nez-Sevilla and L. Sanchez-Gonzalez which generalise (the basic statement of) the classical Whitney extension theorem for C-1-smooth real functions on Rn to the case of real functions on X ([17]) and to the case of mappings from X to Y ([18]) for some Banach spaces X and Y. Since the proof from [18] contains a serious flaw, we supply a different more transparent detailed proof under (probably) slightly stronger assumptions on X and Y. Our proof gives also extensions results from special sets (e.g. Lipschitz submanifolds or closed convex bodies) under substantially weaker assumptions on X and Y. Further, we observe that the mapping F is an element of C-1(X;Y) which extends f given on a closed set A subset of X can be, in some cases, C-infinity-smooth (or C-k-smooth with k > 1) on XA. Of course, also this improved result is weaker than Whitney's result (for X = R-n, Y = R) which asserts that F is even analytic on XA. Further, following another Whitney's article and using the above results, we prove results on extensions of C-1-smooth mappings from open ("weakly") quasiconvex subsets of X. Following the above mentioned articles [17], [18] we also consider the question concerning the Lipschitz constant of F if f is a Lipschitz mapping. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Název v anglickém jazyce
On C1 Whitney extension theorem in Banach spaces
Popis výsledku anglicky
Our note is a complement to recent articles [17] (2011) and [18] (2013) by M. Jim & eacute;nez-Sevilla and L. Sanchez-Gonzalez which generalise (the basic statement of) the classical Whitney extension theorem for C-1-smooth real functions on Rn to the case of real functions on X ([17]) and to the case of mappings from X to Y ([18]) for some Banach spaces X and Y. Since the proof from [18] contains a serious flaw, we supply a different more transparent detailed proof under (probably) slightly stronger assumptions on X and Y. Our proof gives also extensions results from special sets (e.g. Lipschitz submanifolds or closed convex bodies) under substantially weaker assumptions on X and Y. Further, we observe that the mapping F is an element of C-1(X;Y) which extends f given on a closed set A subset of X can be, in some cases, C-infinity-smooth (or C-k-smooth with k > 1) on XA. Of course, also this improved result is weaker than Whitney's result (for X = R-n, Y = R) which asserts that F is even analytic on XA. Further, following another Whitney's article and using the above results, we prove results on extensions of C-1-smooth mappings from open ("weakly") quasiconvex subsets of X. Following the above mentioned articles [17], [18] we also consider the question concerning the Lipschitz constant of F if f is a Lipschitz mapping. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2025
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Journal of Functional Analysis
ISSN
0022-1236
e-ISSN
1096-0783
Svazek periodika
289
Číslo periodika v rámci svazku
9
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
34
Strana od-do
111061
Kód UT WoS článku
001507959000001
EID výsledku v databázi Scopus
2-s2.0-105007165250