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

[摘要] In Chapter I a brief introduction to the basic notions oflocally 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 locallyconvex complex linear topological space (l.t.s). The theory issketched of continuous linear functions on one sequentially completelocally convex complex l.t.s. to a second such space. In the samespirit some theorems relating to functions of several complexvariables taking their values in a sequentially complete locallyconvex complex l.t.s. are developed. In Chapter III, functions onone sequentially complete locally convex complex l.t.s to a secondsuch space are studied and in particular notions of differentiabilityand analyticity. An analogue of the Cauchy-Riemann theory of functionsof a complex variable is discussed.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Mathematics