Complex Function Theory for Functions with Arguments and Values in Locally Convex Linear Topological Spaces

Citation

Bernholtz, Benjamin (1952) Complex Function Theory for Functions with Arguments and Values in Locally Convex Linear Topological Spaces. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NSNX-7J43. https://resolver.caltech.edu/CaltechTHESIS:10042017-091604604

Abstract

In Chapter I a brief introduction to the basic notions of locally convex linear topological spaces is given. In Chapter II, a theory of analytic functions is developed for functions of a complex variable with values in a sequentially complete locally convex complex linear topological space (l.t.s). The theory is sketched of continuous linear functions on one sequentially complete locally convex complex l.t.s. to a second such space. In the same spirit some theorems relating to functions of several complex variables taking their values in a sequentially complete locally convex complex l.t.s. are developed. In Chapter III, functions on one sequentially complete locally convex complex l.t.s to a second such space are studied and in particular notions of differentiability and analyticity. An analogue of the Cauchy-Riemann theory of functions of a complex variable is discussed.

Thesis Files