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010   $a981-10-4205-5
024 7 $a10.1007/978-981-10-4205-8
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035   $a(DE-He213)978-981-10-4205-8
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035   $a(PPN)200511203
035   $a(EXLCZ)993710000001186974
100   $a20170427d2017      u|             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aClassical summability theory$b[electronic resource] /$fby P.N. Natarajan
205   $a1st ed. 2017.
210  1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2017.
215   $a1 online resource (XI, 130 p.)
300   $aIncludes index.
311   $a981-10-4204-7 
327   $aChapter 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.
330   $aThis 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.
606   $aSequences (Mathematics)
606   $aMatrix theory
606   $aAlgebra
606   $aFunctional analysis
606   $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X
606   $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
615  0$aSequences (Mathematics).
615  0$aMatrix theory.
615  0$aAlgebra.
615  0$aFunctional analysis.
615 14$aSequences, Series, Summability.
615 24$aLinear and Multilinear Algebras, Matrix Theory.
615 24$aFunctional Analysis.
676   $a515.24
700   $aNatarajan$b P.N$4aut$4http://id.loc.gov/vocabulary/relators/aut$0980217
906   $aBOOK
912   $a9910254280503321
996   $aClassical Summability Theory$92235918
997   $aUNINA