Two singular point linear Hamiltonian systems with an interface condition

Abstract

We consider the problem of a linear Hamiltionian system on R with an interface condition which we take to be at x = 0. Assuming limit point conditions at /-infinity, we prove the problem is uniquely solvable, and a resolvent is constructed Our method of solution is to map the problem onto a half line problem of double size and apply the theory of half line problems. A Tachmarsh-Weyl function is associated with the problem. and a unitary transform is constructed which maps the differential operator onto the multiplication operator in the Hilbert space determined by the spectral function rho (C) 2010 WILEY-VCH Verlag GmbH & Co KGaA. Weinheim