Abstract
AbstractA symmetric Nevanlinna function Q is of the form Q (z) = zQs (z2) where Qs and Q 0(z) = zQs (z) are also Nevanlinna functions. In such a situation Qs and –Q–10 are Stieltjes functions. An inverse result of L. de Branges implies that each Nevanlinna function is the Titchmarsh–Weyl coefficient of a uniquely determined canonical system with some nonnegative Hamiltonian matrix function H, and, according to M. G. Krein, each Stieltjes function is the Titchmarsh–Weyl coefficient of a uniquely determined string. The Hamiltonians corresponding to Qs , Q0 and Q are constructed in terms of the string corresponding to Qs and the dual string corresponding to –Q–10. The relations between the associated Fourier transformations are described by commuting isometric isomorphisms between the considered spaces. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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