Some Problems in the Application of Functional Analysis to Holomorphy

Publisher Summary This chapter presents a lecture on some of the problems in applying functional analysis to holomorphy. In the discussion greater generality in this exposition is avoided. It is assumed that E, F denote Hausdorff complex locally convex spaces, and U to be a nonvoid open substet of E. The chapter also presents several related definitions and mentions one among them as: E is holomorphically bornological (hbo) if, for every F and U, whenever f: U → F is finitely holomorphic and f is bounded on every compact subset of U, then it follows that f is holomorphic.