Automorphisms and equivalence of tube domains with bounded base (Q1818927)

The author studies the problem of holomorphic and affine equivalences of tube domains with bounded base. The simple examples of such domains are a strip in \(\mathbb C\) and their higher dimensional analogues. It is shown that any tube domain is affinely equivalent to a product of a strip in \(\mathbb C^r\) and a tube domain whose automorphism group coincides with its subgroup of affine transformations. In particular the author proves that two holomorphically equivalent tube domains are also affinely equivalent.