Analytic equivalence of the boundary eigenvalue operator function and its characteristic matrix function
Let T(\(\lambda)\):\(H^ n_ 1(a,b)\Rightarrow L^ n_ 2(a,b)\oplus {\mathbb{C}}^ n\) be the operator defined by the boundary value problem \(f'+A(.,\lambda)f=g\), \(R(\lambda)f=x\). Here \(\lambda\) is a spectral parameter which runs through on open connected set in \({\mathbb{C}}\), and the matrix and operator functions involved are analytic in \(\lambda\). The operator function T(.) is shown to be analytically equivalent on \(\Omega\) to a simple extension of the characteristic matrix function M(.) associated with the boundary value problem. Explicit formulas for the operator functions that establish the equivalence are given. As a corollary the root functions of T(.) are described explicitly in terms of those of the matrix function M(.) [see \textit{R. Mennicken} and \textit{M. Möller}, ibid. 9, 237-265 (1986) for earlier results in this direction].
scientific article; zbMATH DE number 3946951