On nonconvexity of graphs of polynomials of several real variables
Repovš, Dušan, 1954- ; Semenov, Pavel Vladimirovič
Obravnavamo transverzalne (ortogonalne) perturbacije končno-dimenzionalnih konveksnih množic in ocenjujemo "stopnjo nekonveksnosti" ustreznih množic, t.j. ocenjujemo nekonveksnost grafov zveznih ...funkcij. Dokažemo, da primerna ocena nekonveksnosti grafov nad vsemi premicami inducira "lepo" oceno nekonveksnosti grafa cele funkcije, kjer "lepo" pomeni, da v znanem Michaelovem izreku o selekcijah lahko konveksne množice mnogoznačnih preslikav zamenjamo s takimi nekonveksnimi množicami. Kot posledico dobimo pozitivne rezultate za polinome stopnje 2, pri določenih omejitvah za koeficiente. Obravnavamo tudi polinome stopnje 3 in 9.
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