"Neuveden" . . "2"^^ . "P(GA201/07/0388), Z(MSM0021620839)" . . "RIV/00216208:11320/08:00100555!RIV09-MSM-11320___" . "Convexity; Properties; Harmonic; Measures"@en . "11320" . . "Vlastnosti konvexity harmonick\u00FDch m\u011Br"@cs . "Je uk\u00E1z\u00E1no, \u017Ee libovolnou konvexn\u00ED kombinaci harmonick\u00FDch m\u011Br odpov\u00EDdaj\u00EDc\u00EDch kone\u010Dn\u00E9mu syst\u00E9mu otev\u0159en\u00FDch okol\u00ED dan\u00E9ho bodu x lze libovoln\u011B p\u0159esn\u011B aproximovat posloupnost\u00ED harmonick\u00FDch m\u011Br p\u0159\u00EDslu\u0161n\u00FDch posloupnosti otev\u0159en\u00FDch okol\u00ED bodu x obsa\u017Een\u00FDch ve sjednocen\u00ED dan\u00E9ho syst\u00E9mu. T\u00EDm je \u0159e\u0161en otev\u0159en\u00FD probl\u00E9m formulovan\u00FD v souvislosti s Jensenov\u00FDmi m\u00EDrami B.J. Colem T.J.Ransfordem. Tak\u00E9 je dok\u00E1z\u00E1no, \u017Ee pro ka\u017Edou Greenovu mno\u017Einu X obsahuj\u00EDc\u00ED bod x, extrem\u00E1ln\u00ED reprezentuj\u00EDc\u00ED m\u00EDry pro bod x vzhledem ke konvexn\u00EDmu ku\u017Eelu potenci\u00E1l\u016F na X tvo\u0159\u00ED hustou mno\u017Einu kompaktn\u00ED konvexn\u00ED mno\u017Ein\u011B v\u0161ech reprezentuj\u00EDc\u00EDch m\u011Br."@cs . "Convexity Properties of Harmonic Measures"@en . "000256686100007" . . . . "218" . "Convexity Properties of Harmonic Measures" . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . "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\u00B4s." . "Hansen, Wolfhard" . . "RIV/00216208:11320/08:00100555" . "Netuka, Ivan" . "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\u00B4s."@en . . "[D6953188F122]" . . . "Vlastnosti konvexity harmonick\u00FDch m\u011Br"@cs . . . . "43"^^ . "0001-8708" . "361305" . "Convexity Properties of Harmonic Measures"@en . . . "Convexity Properties of Harmonic Measures" . "Advances in Mathematics" . . . "1"^^ .