Year: 2017
Type: preprint
Abstract: R. Guralnick (Linear Algebra Appl. 99, 85-96, 1988) proved that two holomorphic matrices on a noncompact connected Riemann surface, which are locally holomorphically similar, are globally holomorphically similar. We generalize this to (possibly, non-smooth) one-dimensional Stein spaces. For Stein spaces of arbitrary dimension, we prove that global $\mathcal C^\infty$ similarity implies global holomorphic similarity, whereas global continuous similarity is not sufficient.
Source: arXiv (Cornell University)
Author: Leiterer, Jürgen
Institution: Humboldt-Universität zu Berlin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952592289