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/NSNX7J43. https://resolver.caltech.edu/CaltechTHESIS:10042017091604604
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 CauchyRiemann theory of functions of a complex variable is discussed.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Mathematics 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1952 
Record Number:  CaltechTHESIS:10042017091604604 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:10042017091604604 
DOI:  10.7907/NSNX7J43 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  10481 
Collection:  CaltechTHESIS 
Deposited By:  Benjamin Perez 
Deposited On:  04 Oct 2017 17:01 
Last Modified:  20 Dec 2019 20:00 
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