Citation
Reed, Irving S. (1949) Quadratic differential equations in Banach spaces and analytic functionals. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd06242004135659
Abstract
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In Chapter I the preliminary concepts are introduced and applied to the quadratic differential equations, [...], in a complete normed linear ring. In Chapters II and V the functional equation, [...] is studied under suitable assumptions and shown to be related to the Frechet differential of the above differential equation as a functional of [...]. In Chapter IV the more general functional equation, [...], where T is an endomorphism, is treated.
The existence of the Frechet differential with respect to [...] is shown in Chapter II by means of a power series for the solution of [...] where Q is a trilinear function. The solution of [...] is obtained in Chapter VI in the terminology of Chapter IV. Moreover, the solution is shown to satisfy unquely the differential system, [...], [...] and to possess a generalized Taylor series expansion. The above equation is generalized with similar results to [...], where T is a trilinear function.
Chapter VII is concerned with examples of Chapter VI. For instance, the solution of the matrix differential equation, [...], [...], is treated both as a function of [...] and as an analytic functional of the [...] continuous functions [...].
Item Type:  Thesis (Dissertation (Ph.D.)) 

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 1949 
Record Number:  CaltechETD:etd06242004135659 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd06242004135659 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2710 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  28 Jun 2004 
Last Modified:  26 Dec 2012 02:53 
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