关于在扇形域内正定的二次型

ON POSITIVE DEFINITE QUADRATIC FORM IN A REGION OF SECTOR

本文给出二次型在扇形域内正定性的若干充要条件.

We say that the quadratic form F(x,§_1,§_2)is positive definitein a region of sector §(μ C^I x—§)≥0(j=1,2)ifF(x,§_1,§_2)>0 for §,(μ,C^Ix,—§)≥0,|x|+|§_1|+|§_2|≠0.n this paper,we give some necessary and sufficient conditions for positivedefiniteness of quadratic form in a region of sector.