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  • Je ukázáno, že libovolnou konvexní kombinaci harmonických měr odpovídajících konečnému systému otevřených okolí daného bodu x lze libovolně přesně aproximovat posloupností harmonických měr příslušných posloupnosti otevřených okolí bodu x obsažených ve sjednocení daného systému. Tím je řešen otevřený problém formulovaný v souvislosti s Jensenovými mírami B.J. Colem T.J.Ransfordem. Také je dokázáno, že pro každou Greenovu množinu X obsahující bod x, extremální reprezentující míry pro bod x vzhledem ke konvexnímu kuželu potenciálů na X tvoří hustou množinu kompaktní konvexní množině všech reprezentujících měr. (cs)
  • It is shown that any convex combination of harmonic meaures corresponding to a finite family of open neighborhoods of the given point x can be approximated by a sequence of harmonic measures corresponding to a sequence of open neighborhoods of x in the union of the given family. This solves an open problem raised in connection with Jensen measures by B.J.Cole and T.J. Ransford. It is also proved that, for every Green domain X containing x, the extremal representing measures for x with respect to the convex cone of potentials on X are dense in the compact convex set of all representing measures. Results are presented simultaneously for the classical potential theory and for the theory of Riesz potentials. Also, very general potential-theoretic setting covering a wide class of second order PDE´s.
  • It is shown that any convex combination of harmonic meaures corresponding to a finite family of open neighborhoods of the given point x can be approximated by a sequence of harmonic measures corresponding to a sequence of open neighborhoods of x in the union of the given family. This solves an open problem raised in connection with Jensen measures by B.J.Cole and T.J. Ransford. It is also proved that, for every Green domain X containing x, the extremal representing measures for x with respect to the convex cone of potentials on X are dense in the compact convex set of all representing measures. Results are presented simultaneously for the classical potential theory and for the theory of Riesz potentials. Also, very general potential-theoretic setting covering a wide class of second order PDE´s. (en)
Title
  • Convexity Properties of Harmonic Measures
  • Convexity Properties of Harmonic Measures (en)
  • Vlastnosti konvexity harmonických měr (cs)
skos:prefLabel
  • Convexity Properties of Harmonic Measures
  • Convexity Properties of Harmonic Measures (en)
  • Vlastnosti konvexity harmonických měr (cs)
skos:notation
  • RIV/00216208:11320/08:00100555!RIV09-MSM-11320___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/07/0388), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • Neuveden
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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  • 361305
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/08:00100555
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Convexity; Properties; Harmonic; Measures (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [D6953188F122]
http://linked.open...i/riv/nazevZdroje
  • Advances in Mathematics
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http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 218
http://linked.open...iv/tvurceVysledku
  • Netuka, Ivan
  • Hansen, Wolfhard
http://linked.open...ain/vavai/riv/wos
  • 000256686100007
http://linked.open...n/vavai/riv/zamer
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  • 0001-8708
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  • 11320
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