Picard Dimension of Signed Radial Kato Measures
English Series · 2009
The Picard dimension dimµ of a signed local Kato measure µ on the punctured unit ball in R d , d ≥ 2, is the cardinal number of the set of extremal rays of the convex cone of all continuous solutions u ≥ 0 of the time-independent Schrodinger equation Δu − uµ = 0 on the punctured ball 0 < � x� < 1, with vanishing boundary values on the spherex� = 1. Using potential theory associated with the Schrodinger operator we prove, in this paper, that the dimµ for a signed radial Kato measure is 0, 1o r + ∞. In particular, we obtain the Picard dimension of locally Holder continuous functions P proved by Nakai and Tada by other methods.