Decomposition of meromorphic Fredholm resolvents and \(\Psi^*\)-algebras
The authors consider meromorphic resolvents of analytic (semi-) Fredholm operator functions M on (Stein) regions in \({\mathbb{C}}^ N\). The main problem is a decomposition \(M=A+S\) where A is holomorphic and S is meromorphic with special properties. Previous results are due to \textit{B. Gramsch} [Math. Z. 133, 219-242 (1973; Zbl 0254.47043)] and (sharpened) \textit{H. Bart}, \textit{W. Kaballo} and \textit{G. P. A. Thiejsse} [Integral equations Oper. Theory 3, 1-22 (1980; Zbl 0435.47023)]. The paper presents a further sharpened decomposition theorem, in some sense, pointed out in the paper, a best possible result.
meromorphic resolvents of analytic (semi-) Fredholm operator functions on (Stein) regions
scientific article; zbMATH DE number 4132944