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| rdf:type
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| 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. (cs)
- 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 such a 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 for mappings 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.
- 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 such a 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 for mappings 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. (en)
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| Title
| - Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces
- Přesné vyplňování množin s pomocí derivací hladkých zobrazení mezi Banachovými prostory (cs)
- Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces (en)
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| skos:prefLabel
| - Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces
- Přesné vyplňování množin s pomocí derivací hladkých zobrazení mezi Banachovými prostory (cs)
- Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces (en)
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| skos:notation
| - RIV/67985840:_____/05:00079355!RIV07-AV0-67985840
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| http://linked.open.../vavai/riv/strany
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(GA201/01/1198), P(IAA1019003), Z(AV0Z10190503)
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| http://linked.open...iv/cisloPeriodika
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
| |
| http://linked.open...ai/riv/idVysledku
| - RIV/67985840:_____/05:00079355
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - n-times smooth; Fréchet smooth; Gateaux smooth bump (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...odStatuVydavatele
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/nazevZdroje
| - Canadian Mathematical Bulletin-Bulletin Canadien de Mathematiques
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...v/svazekPeriodika
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| http://linked.open...iv/tvurceVysledku
| - Fabian, Marián
- Azagra, D.
- Jiménez-Sevilla, M.
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| http://linked.open...n/vavai/riv/zamer
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| issn
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| number of pages
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| is http://linked.open...avai/riv/vysledek
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