a1 Department of Analysis and Technical Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/114, A-1040 Wien, Austria ([email protected])
We consider a family of self-adjoint 2 × 2-block operator matrices Ã in the space L2(0, 1) L2(0, 1), depending on the real parameter . If Ã0 has an eigenvalue that is embedded in the essential spectrum, then it is shown that for ≠ 0 this eigenvalue in general disappears, but the resolvent of Ã has a pole on the unphysical sheet of the Riemann surface. Such a pole is called a resonance pole. The unphysical sheet arises from analytic continuation from the upper half-plane C+ across the essential spectrum. Furthermore, the asymptotic behaviour of this resonance pole for small is investigated. The results are proved by considering a certain λ-rational Sturm–Liouville problem and its Titchmarsh–Weyl coefficient.
(Received November 15 1999)
(Accepted May 18 2000)