Abstract
We investigate the structure of a maximal chain of matrix functions whose Weyl coefficient belongs to \( \mathcal{N}_\kappa ^ + \) . It is shown that its singularities must be of a very particular type. As an application we obtain detailed results on the structure of the singularities of a generalized string which are explicitly stated in terms of the mass function and the dipole function. The main tool is a transformation of matrices, the construction of which is based on the theory of symmetric and semibounded de Branges spaces of entire functions. As byproducts we obtain inverse spectral results for the classes of symmetric and essentially positive generalized Nevanlinna functions.Keywordsgeneralized stringchain of matricesde Branges space
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