Summary: The Kre*in-Langer integral representation of a matrix-valued generalized Nevanlinna function arises in problems of spectral theory and interpolation. A version of this formula which is suitable for such problems, and a corresponding Stieltjes inversion formula, are derived. Some classes of generalized Nevanlinna functions which are defined in terms of behavior at infinity are characterized in terms of their integral representations.

47A56

generalized Nevanlinna function, matrix-valued function, integral representation, Stieltjes inversion formula, negative squares