Characterizations of generalized poles by pole cancellation functions of higher order

2013/09/30 by Muhamed Borogovac, Annemarie Luger · 4 citations
Mathematics · #Holomorphic and Operator Theory #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics #math.FA #msc:30E99 #msc:46C20 #msc:47B50

paper · pdf · doi:10.1016/j.jfa.2014.09.025

published as Journal of Functional Analysis 267 (2014), pp. 4499-4518

arxiv created 2014/10/10 · arxiv updated 2014/10/27

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 ℓ, we show that there exists a pole cancellation function of order at least ℓ, and, moreover, this function is of surprisingly simple form.

Cited by

• Construction of Pole Cancellation Functions at Ordinary Poles of Operator-Valued Functions
• Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps
• Desirable Decompositions of Generalized Nevanlinna Functions
• Root functions of a meromorphic matrix function and applications