Doctoral Dissertations


“Classical Tauberian theory studies sequences {un} 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 {un}. 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 {un}.

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.


Stanojevic, Caslav V., 1928-2008

Committee Member(s)

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


Mathematics and Statistics

Degree Name

Ph. D. in Mathematics


University of Missouri--Rolla

Publication Date

Summer 2002


v, 44 pages

Note about bibliography

Includes bibliographical references (pages 42-43).


© 2002 Fi̇li̇z Di̇k, All rights reserved.

Document Type

Dissertation - Restricted Access

File Type




Subject Headings

Tauberian theorems
Sequences (Mathematics)

Thesis Number

T 8089

Print OCLC #


Link to Catalog Record

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