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A symmetric Nevanlinna function Q is of the form Q(z) = zQs(z 2 ) where Qs and Q0(z) = zQs(z) are also Nevanlinna functions. In such a situation Qs and −Q −1 0 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 −1 0 . The relations between the associated Fourier transformations are described by commuting isometric isomorphisms between the considered spaces.

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