Doctoral Dissertations

Abstract

"We will determine necessary and sufficient conditions for the existence of analytic solutions of the nonhomogeneous nth order differential equation at a singular point. Let An be the Banach space of complex functions analytic in the open unit disk and n times continuously differentiable on the closed unit disk. Let L: An -+ A0 be a linear Fuchsian differential operator with coefficients in A0. If L* denotes the operator conjugate to L, then we will use the theory of normally solvable and Noetherian operators to show that the dimension of the kernel of L is equal to the dimension of the kernel of L *. Certain representation theorems from functional analysis will be used to describe the space of linear functionals that contain the kernel of L*. These results will be used to derive a form of the Fredholm Alternative that will establish a link between the solvability of Ly = g at a singular point and the kernel L*. The relationship between the roots of the indicial equation associated with Ly = 0 and the kernel of L* will allow us to show that the kernel of L* is spanned by a set of polynomials. Finally, examples will be given that illustrate these results"-- Abstract, p. iii

Advisor(s)

Hall, Leon M., 1946-

Committee Member(s)

Grimm, L. J., -2010
Clark, Stephen L.
Hering, Roger H.
Okunbor, Daniel I.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

Summer 1997

Pagination

iv, 31 pages

Note about bibliography

Includes bibliographical references (pages 29-30)

Rights

© 1997 Brian Douglas Haile, All rights reserved.

Document Type

Dissertation - Restricted Access

File Type

text

Language

English

Thesis Number

T 7362

Print OCLC #

39636387

Download
Off-campus S&T users

Share My Dissertation If you are the author of this work and would like to grant permission to make it openly accessible to all, please click the button above.

Share

 
COinS