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Classical Summability Theory (Hardcover, 1st ed. 2017)
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Classical Summability Theory (Hardcover, 1st ed. 2017)
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This book presents results about certain summability methods, such
as the Abel method, the Norlund method, the Weighted mean method,
the Euler method and the Natarajan method, which have not appeared
in many standard books. It proves a few results on the Cauchy
multiplication of certain summable series and some product
theorems. It also proves a number of Steinhaus type theorems. In
addition, it introduces a new definition of convergence of a double
sequence and double series and proves the Silverman-Toeplitz
theorem for four-dimensional infinite matrices, as well as Schur's
and Steinhaus theorems for four-dimensional infinite matrices. The
Norlund method, the Weighted mean method and the Natarajan method
for double sequences are also discussed in the context of the new
definition. Divided into six chapters, the book supplements the
material already discussed in G.H.Hardy's Divergent Series. It
appeals to young researchers and experienced mathematicians who
wish to explore new areas in Summability Theory..
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