Journal of Operator Theory

Volume 48, Issue 1, Summer 2002 pp. 187-226.

Factorization theorem for transfer function associated with a $ 2\times 2$ operator matrix having unbounded couplings

Authors: Volker Hardt (1), Reinhard Mennicken (2), and Alexander K. Motovilov (3)
Author institution: (1) Department of Mathematics, University of Regensburg, D-93040 Regensburg, Germany
(2) Department of Mathematics, University of Regensburg, D-93040 Regensburg, Germany
(3) Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia

Summary: We construct operators which factorize the transfer function associated with a self-adjoint $2\times2$ operator matrix whose diagonal entries may have overlapping spectra and whose off-diagonal entries are unbounded operators. We prove completeness and basis properties of the eigenvectors of the transfer function corresponding to the real point spectrum of the $2\times2$ operator matrix. We also discuss some properties of the root vectors of the analytically continued transfer function.

Keywords: Operator matrix, operator pencil, Herglotz function, resonance

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