Tauberian Theorems for Certain Regular Processes Page: 4
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In 1958 F. K. Keogh and G. M. Petersen were able to
extend Buck's result by showing that x is convergent if
some regular matrix A sums a set of subsequences of x which
is of the second category. The fourth chapter of this
paper contains analogs to this theorem in which the re-
quirement of regularity is weakened somewhat. In addition,
the sequence space Z, as well as c, is investigated, and
rearrangements as well as subsequences are considered.
Typical of the results in Chapter IV are theorems which
show that a sequence x is convergent if there exists a
non-Schur matrix A with convergent columns that sums a set
of subsequences (rearrangements) which is of the second
category.
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Keagy, Thomas A. Tauberian Theorems for Certain Regular Processes, dissertation, August 1975; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc501087/m1/4/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .