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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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics and Physics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Michal, Aristotle D.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1952
Record Number:CaltechTHESIS:10042017-091604604
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:10042017-091604604
DOI:10.7907/NSNX-7J43
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:10 May 2023 22:41

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