Citation
Swanson, Charles Andrew (1957) Asymptotic Expansions for Characteristic Values and Functions of a Second Order Ordinary Linear Differential Operator. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NSHV8P43. https://resolver.caltech.edu/CaltechETD:etd08062004144733
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Consider a second order ordinary linear differential operator on a real halfopen interval (0,b] (b > 0) which contains no singular points. Suppose x = 0 is a singular point. The basic characteristic value problem is defined on this interval when suitable boundary conditions are adjoined at the endpoints. Two classes of perturbed characteristic value problems are defined on subintervals [a,b], where a is a small positive number. It is proved under certain conditions on the basic problem that for each isolated characteristic value [...] of the basic problem there is a characteristic value [...] of the perturbed problem which is developable in an asymptotic expansion with leading term [...] valid as [...]. Furthermore, the characteristic function corresponding to [...] possesses an asymptotic expansion valid as [...] uniformly in the interval [a,b]. These expansions are not asymptotic power series, but are asymptotic expansions of a more general type.
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): 

Thesis Committee: 

Defense Date:  1 January 1957 
Record Number:  CaltechETD:etd08062004144733 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd08062004144733 
DOI:  10.7907/NSHV8P43 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3023 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  09 Aug 2004 
Last Modified:  20 Dec 2019 19:39 
Thesis Files

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