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.

Cauchy domains, Logarithmic residues, analytic Banach algebra valued function, meromorphic inverse
hdl.handle.net/1765/1671
Econometric Institute Research Papers
Erasmus School of Economics

Bart, H, Ehrhardt, T, & Silbermann, B. (2001). Logarithmic residues of analytic Banach algebra valued functions possessing a simply meromorphic inverse (No. EI 2001-06). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/1671