Characterizations of generalized poles by pole cancellation functions of higher order

Abstract

In this paper the analytic characterization of generalized poles of operator valued generalized Nevanlinna functions (including the length of Jordan chains of the representing relation) is completed. In particular, given a Jordan chain of length $\ell$, we show that there exists a pole cancellation function of order at least $\ell$, and, moreover, this function is of surprisingly simple form.

Cited by in corpus (5)

• Inverse of generalized Nevanlinna function that is holomorphic at infinity
• Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps
• Novel approach to root functions of matrix polynomials with applications in differential equations and meromorphic matrix functions
• Desirable Decompositions of Generalized Nevanlinna Functions
• Construction of Pole Cancellation Functions at Ordinary Poles of Operator-Valued Functions