Subordinate Solutions and Spectral Measures of Canonical Systems

The theory of 2 × 2 trace-normed canonical systems of differential equations on R+ can be put in the framework of abstract extension theory. This includes the theory of strings as developed by I.S. Kac and M.G. Kreĭn. In the present paper the spectral properties of such canonical systems are characterized by means of subordinate solutions. The theory of subordinacy for Schrödinger operators on the halfline R+, was originally developed D.J. Gilbert and D.B. Pearson. Its extension to the framework of canonical systems makes it possible to describe the spectral measure of any Nevanlinna function in terms of subordinate solutions of the corresponding trace-normed canonical system, which is uniquely determined by a result of L. de Branges.