Abstract:
operator, (Dunford and Schwartz,
1957) pp. 593 - 597. It is evident from the mentioned books that a Tauberian theory
for N¨orlund operators is almost non-existent. Therefore we are confident the results
x
developed in the thesis will open a floodgate for such theorems for N¨orlund means. In
turn this will find application in diverse fields such as, integral transforms and Fourier
analysis; and in probability and statistics through such areas involving central limit
theorem, almost sure convergence, summation of random series, Markov chains e.t.c;
(Boos, 2000) pp. 256 - 257.
Chapter 1 deals with literature review, a summary of Functional Analysis material;
as well as classical summability methods; especially those that are pertinent to
our study.
Chapter II deals with the spectrum of the Q matrix on c0 and c. In chapter III
we investigate the spectrum of the N¨orlund Q operator on the spaces bv0 and bv.
Chapter IV is concerned with the fine spectrum of the Q matrix operator on c. In
Chapter V we investigate the spectrum of an almost N¨orlund Q matrix operator on
c0 and c. Chapter VI gives an overview of the results obtained and points the way
forward for future research interests.
In achieving the results, we used a combination of classical and modern functional
analytic methods as well as Summability methods. Functional analytic methods usually
appeal to the powerful Banach space theorems, such as Hahn - Banach; Banach-
Steinhaus; exetra. Classical Summability methods employ sequence space mapping
theorems such as Silverman - Toeplitz; Kojima - Shur; exetra.
