The Abstract Titchmarsh-weyl M-function for Adjoint Operator Pairs and Its Relation to the Spectrum
نویسندگان
چکیده
In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M -function see the same singularities as the resolvent of a certain restriction AB of the maximal operator? We obtain results showing that it is possible to describe explicitly certain spaces S and S̃ such that the resolvent bordered by projections onto these subspaces is analytic everywhere that the M -function is analytic. We present four examples – one involving a Hain-Lüst type operator, one involving a perturbed Friedrichs operator and two involving a simple ordinary differential operators on a half line – which together indicate that the abstract results are probably best possible. AMS(MOS) Subject Classifications: 35J25, 35P05, 47A10, 47A11
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