Generalized zeros and poles of N_κ-functions: on the underlying spectral structure - Luger, A.; Hassi, S. (Methods of Functional Analysis and Topology, 2006)
Let q be a scalar generalized Nevanlinna function, qN_κ. Its gene alized zeros and poles (including their orders) are defined in terms of the function’s operator representation. In this paper analytic properties associated with the underlying root subspaces and their geometric structures are investigated in terms of the local behaviour of the function. The main results and various characterizations are expressed by means of (local) moments, asymptotic expansions, and via the basic factorization of q. Also an inverse problem for recovering the geometric structure of the root subspace from an appropriate asymptotic expansion is solved.