---

＜E-Book＞
Classical Summability Theory / by P.N. Natarajan

Edition	1st ed. 2017.
Publisher	(Singapore : Springer Nature Singapore : Imprint: Springer)
Year	2017
Language	English
Size	XI, 130 p : online resource
Authors	*Natarajan, P.N author SpringerLink (Online service)
Subjects	LCSH:Sequences (Mathematics) LCSH:Algebras, Linear LCSH:Functional analysis FREE:Sequences, Series, Summability FREE:Linear Algebra FREE:Functional Analysis
Notes	Chapter 1. Brief Introduction, General Summability Theory and Steinhaus Type Theorems -- Chapter 2. Core of a Sequence and the Matrix Class -- Chapter 3. Special Summability Methods -- Chapter 4. More Properties of the Method and Cauchy Multiplication of Certain Summable Series -- Chapter 5. The Silverman-Toeplitz, Schur's and Steinhaus Theorems for 4-dimensional Infinite Matrices -- Chapter 6. The Norlund, Weighted Mean and Methods for Double Sequences 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 areasin Summability Theory HTTP:URL=https://doi.org/10.1007/978-981-10-4205-8

 Similar Items