Sturm-Liouville systems with rational Weyl functions: Explicit formulas and applications (Q1384116)

The authors solve explicitly direct and inverse spectral problems for Sturm-Liouville systems with rational Weyl functions, of the form \[ {d^2\over dx^2} f(x,\lambda)- u(x)f(x, \lambda)+ \lambda f(x,\lambda)= 0\tag{1} \] on the half axis \(x\geq 0\); \(f\) is a \(\mathbb{C}^m\)-valued function, \(u\) is an \(m\times m\) locally summable matrix function on \([0,+\infty)\) and \(\lambda\) is a complex spectral parameter. With system (1), the authors associate the symmetric operator \(H_0\) defined by \[ (H_0 f)(x):= -{d^2\over dx^2} f(x)+ u(x)f(x),\quad x\geq 0 \] and consider the spectral theory to (1) in terms of an isometric diagonalizing operator \(U\) such that \((U H_0f)(z)= z(Uf)(z)\).