Construction of Pole Cancellation Functions at Ordinary Poles of Operator-Valued Functions

2026/06/30 by Muhamed Borogovac
Mathematics · #math.CV #math.FA

paper · pdf · doi:10.1007/s40627-026-00211-6

Abstract

A pole of order m ∈ ℕ at β∈ ℂ of a regular operator valued function Q : D(Q) → L(H) is investigated. We provide a characterization of pole cancellation functions \boldsymbolψ(z) of Q(z) of order k ≤ m at β in terms of the coefficients of the Laurent expansion of Q. This characterization yields practical and explicit constructions of pole cancellation functions \boldsymbolψ(z). Moreover, it leads to an explicit formula for the associated functions \boldsymbolφ(z) := Q(z)\boldsymbolψ(z), which are root functions of order k at the zero β of Q^-1. The results are illustrated by an example.

Citations

• Characterizations of generalized poles by pole cancellation functions of higher order

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