Large linear manifolds of noncontinuable boundary-regular holomorphic functions

We prove in this paper that if G is a domain in the complex plane satisfying appropriate topological or geometrical conditions, then there exists a large (dense or closed infinite-dimensional) linear submanifold of boundary-regular holomorphic functions on G all of whose nonzero members are not continuable across any boundary point of G. © 2007 Elsevier Inc. All rights reserved.