Logarithmic residues of analytic Banach algebra valued functions possessing a simply meromorphic inverse

Harm Bart, Torsten Ehrhardt and Bernd Silbermann

No EI 2001-06, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: A logarithmic residue is a contour integral of a logarithmic derivative (left or right) of an analytic Banach algebra valued function. For functions possessing a meromorphic inverse with simple poles only, the logarithmic residues are identified as the sums of idempotents. With the help of this observation, the issue of left versus right logarithmic residues is investigated, both for connected and nonconnected underlying Cauchy domains. Examples are given to elucidate the subject matter.

Keywords: Cauchy domains; Logarithmic residues; analytic Banach algebra valued function; meromorphic inverse (search for similar items in EconPapers)
Date: 2001-03-20
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