Recursion Operator and the Trace Formula for 1-dimensional Schrodinger Operator

By using the recursion operator R(u)=∂^<-1>(2^<-1>u^l+u∂-4^<-1>1∂^3), various kind of the trace formulae for the 1-dimentional Schodinger operator H(u)=-∂^2+u(x) are proved. A notion of rank of the function with respect to R(u) is introduced. Moreover, an alternative proof of the characterization theorem of the reflectionless potentials is given.

公開日:2010年1月24日で登録したコンテンツは、国立情報学研究所において電子化したものです。