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A Nevanlinna function is a function which is analytic in the open upper half plane and has a non-negative imaginary part there. In this paper we study a fractional linear transformation for a Nevanlinna function n with a suitable asymptotic expansion at ∞, that is an analogue of the Schur transformation for contractive analytic functions in the unit disc. Applying the transformation p times we find a Nevanlinna function np which is a fractional linear transformation of the given function n. The main results concern the effect of this transformation to the realizations of n and np, by which we mean their representations through resolvents of self-adjoint operators in Hilbert space. Our tools are block operator matrix representations, u--resolvent matrices, and reproducing kernel Hilbert spaces.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Operator Theory: Advances and Applications, volume 190, in 2009 following peer review. The final publication is available at Springer via DOI: 10.1007/978-3-7643-9919-1_4

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