Canonical systems with selfadjoint interface conditions
by
Henrik Winkler
University of Groningen
Coauthors: Henk de Snoo (University of Groningen)

Two-dimensional canonical systems of differential equations Jy'=-zHy on the real line are considered with selfadjoint interface conditions at 0. If one or both of the intervals around 0 are H-indivisible the interface conditions which give rise to selfadjoint relations (multi-valued operators) are determined. The multi-valued part is characterized in terms of the spectral matrix. It is shown that the corresponding generalized Fourier transforms are partially isometric. Compression to the positive halfline leads to Fourier transforms that are isometric except possibly on a one-dimensional subspace where they are contractive.

Date received: May 31, 2002