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  • Pro zadaná přirozená čísla k,n, kde n je liché, ukážeme existenci čísla N = N(k,n) s následující vlastností. Pro každý n-homogenní polynom zadaný na Euklidovském prostoru dimenze N, existuje k-dimenzionální lineární podprostor, na němž se polynom anuluje. (cs)
  • Let k, n .. N, where n is odd. We show that there is an integer N = N(k,n) such that for every n-homogeneous polynomial P : RN .. R there exists a linear subspace X .. RN, dim X = k, such that P|x .IDENT. 0. This quantitative estimate improves on previous work of Birch et al., who studied this problem from an algebraic viewpoint. The topological method of proof presented here also allows us to obtain a partial solution to the Gromov-Milman problem (in dimension two) on an isometric version of a theorem of Dvoretzky.
  • Let k, n .. N, where n is odd. We show that there is an integer N = N(k,n) such that for every n-homogeneous polynomial P : RN .. R there exists a linear subspace X .. RN, dim X = k, such that P|x .IDENT. 0. This quantitative estimate improves on previous work of Birch et al., who studied this problem from an algebraic viewpoint. The topological method of proof presented here also allows us to obtain a partial solution to the Gromov-Milman problem (in dimension two) on an isometric version of a theorem of Dvoretzky. (en)
Title
  • Zero sets of polynomials in several variables
  • Nulové množiny polynomu několika proměnných (cs)
  • Zero sets of polynomials in several variables (en)
skos:prefLabel
  • Zero sets of polynomials in several variables
  • Nulové množiny polynomu několika proměnných (cs)
  • Zero sets of polynomials in several variables (en)
skos:notation
  • RIV/67985840:_____/06:00076206!RIV07-AV0-67985840
http://linked.open.../vavai/riv/strany
  • 561;568
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/01/1198), P(GA201/04/0090), P(IAA1019205), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika
  • 6
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 509838
http://linked.open...ai/riv/idVysledku
  • RIV/67985840:_____/06:00076206
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • polynomial; zero set (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CH - Švýcarská konfederace
http://linked.open...ontrolniKodProRIV
  • [CDD38A59BF3A]
http://linked.open...i/riv/nazevZdroje
  • Archiv der Mathematik
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 86
http://linked.open...iv/tvurceVysledku
  • Hájek, Petr Pavel
  • Aron, R. M.
http://linked.open...n/vavai/riv/zamer
issn
  • 0003-889X
number of pages
is http://linked.open...avai/riv/vysledek of
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