Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F05%3A00079355" target="_blank" >RIV/67985840:_____/05:00079355 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces
Original language description
We establish sufficient conditions on the shape of a set A included in the space L n,s(X,Y) of the n-linear symmetric mappings between Banach spaces X and Y, to ensure the existence of a Cn-smooth mapping f:X - Y with bounded support, and such that f(n)(X) = A, provided that X admits a Cn-smooth bump with bounded n-th derivative and dens X = dens Ln(X,Y). For instance, when X is infinite-dimensional, every bounded connected and open set U containing the origin is the range of the n-th derivative of sucha mapping. The same holds true for the closure of U, provided that every point in the boundary of U is the end point of a path within U. In the finite-dimensional case, more restrictive conditions are required. We also study the Fréchet smooth case formappings from Rn to a separable infinite-dimensional Banach space and the Gâteaux smooth case for mappings defined on a separable infinite-dimensional Banach space and with values in a separable Banach space.
Czech name
Přesné vyplňování množin s pomocí derivací hladkých zobrazení mezi Banachovými prostory
Czech description
Nalézáme postačující podmínky na tvar množiny A nacházející se v prostoru n-lineárních symetrických zobrazení z Banachova prostoru X do Banachova prostoru Y takové, že existuje C^n-hladké zobrazení f z X do Y s vlastností, jeho n-té derivace vyplňují přesně množinu A. Také studujeme případ fréchetovské hladkosti zobrazení z R^n do separabilního Banachova prostoru a gateauxovské hladkosti zobrazení ze separabilního prostoru do separabilního prostoru.
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Canadian Mathematical Bulletin-Bulletin Canadien de Mathematiques
ISSN
0008-4395
e-ISSN
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Volume of the periodical
48
Issue of the periodical within the volume
4
Country of publishing house
CA - CANADA
Number of pages
19
Pages from-to
481-499
UT code for WoS article
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EID of the result in the Scopus database
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