Mina Farag: Characterization of Rational Herglotz Functions

Abstract.

In this thesis, we study rational scalar-valued Herglotz functions. Properties of the class of general Herglotz functions are discussed with examples. Rational scalar-valued Herglotz functions will then be characterised either by the their poles or by the corresponding measures in the integral representation. Lastly, the result from the scalar-valued case is used to extend the result to matrix-valued Herglotz functions.