Uniformly holomorphic continuation in locally convex spaces

Abstract

We investigate the simultaneous uniformly holomorphic continuation of the uniformly holomorphic functions defined in a domain spread of uniform type, ( X, ϑ), over a locally convex Hausdorff space E. We construct the envelope of uniform holomorphy of ( X, ϑ) with an analogous method of the results of M. Schottenloher ( Portugal. Math. 33 (1974)) . Finally, we use this construction to the problem of extending uniformly holomorphic maps f: ( X, ϑ) → F, with values in a complete locally convex space to the envelope of uniform holomorphy of X.