Work

The Product/Sum Identity for Logarithmic Residues in Higher Dimensions

Year: 2026

Type: article

Abstract: In the scalar case, the logarithmic residue of the product fg of two analytic functions f and g is the sum of the logarithmic residues of f and g . Here attention is paid to what happens in the higher dimensional situation where f and g have values in a complex Banach algebra. In the context of giving some background information on vector-valued logarithmic residues, a couple of open problems are indicated.

Source: Integral Equations and Operator Theory

DOI: 10.1007/s00020-026-02857-7

Authors: Harm Bart, Torsten Ehrhardt, Bernd Silbermann

Institutions: Erasmus University Rotterdam, University of California, Santa Cruz, Chemnitz University of Technology

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

OpenAlex ID: W7225075326