Tauberian theorems for convergence and subsequential convergence of sequences with controlled oscillatory behavior

Author

Fi̇li̇z Di̇k

Abstract

“Classical Tauberian theory studies sequences {u_n} whose divergence is manageable. The main objective of the theory is to recover convergence of such sequences out of the existence of certain limits and some additional conditions that control the oscillatory behavior of {u_n}. However, there are some conditions of considerable interest from which it is not possible to obtain convergence of the sequence. This situation motivates a different kind of Tauberian theory where we do not look for the convergence recovery of the sequence. Rather, we are concerned with the subsequential behavior of the sequence {u_n}.

Succinct proofs of the Hardy-Littlewood theorem and the generalized Littlewood theorem are given using the significant corollary to Karamata’s Hauptsatz. Subsequential Tauberian theory is introduced and related Tauberian theorems are proved. Also, convergence and subsequential convergence of regularly generated sequences are studied”--Abstract, page iii.

Advisor(s)

Stanojevic, Caslav V., 1928-2008

Committee Member(s)

Hall, Leon M., 1946-
Hering, Roger H.
Randolph, Timothy W.
Gelles, Gregory M.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

Summer 2002

Pagination

v, 44 pages

Note about bibliography

Includes bibliographical references (pages 42-43).

Rights

© 2002 Fi̇li̇z Di̇k, All rights reserved.

Document Type

Dissertation - Restricted Access

File Type

text

Language

English

Subject Headings

Tauberian theoremsSequences (Mathematics)

Thesis Number

T 8089

Print OCLC #

52545454

Recommended Citation

Di̇k, Fi̇li̇z, "Tauberian theorems for convergence and subsequential convergence of sequences with controlled oscillatory behavior" (2002). Doctoral Dissertations. 1443.
https://scholarsmine.mst.edu/doctoral_dissertations/1443