For any function belonging to the class of Nevanlinna functions, the function defined by belongs to for all values of . The class possesses subclasses , each defined by some additional asymptotic conditions. If a function belongs to such a subclass, then for all but one value of the function belongs to the same subclass and the corresponding exceptional function can be characterized (cf. ). In this note we introduce two subclasses of which can be described in terms of the moments of the spectral measures in the associated integral representations. We characterize the corresponding exceptional function in a purely function-theoretic way by suitably estimating certain quadratic terms. The behaviour of the exceptional function connects the subclasses and to the classes and , respectively, as studied in . In operator-theoretic terms these notions have a translation in terms of -functions of selfadjoint extensions of a symmetric operator with defect numbers (1, 1). In this sense the exceptional function has an interpretation in terms of a generalized Friedrichs extension of the symmetric operator.
Cite this article
S. Hassi, Jaap Top, On some Subclasses of Nevanlinna Functions. Z. Anal. Anwend. 15 (1996), no. 1, pp. 45–55