Classical Summability Theory

Authors: Natarajan, P.N.

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  • Focuses on recent topics in classical summability theory
  • Is a valuable resource for mathematicians, engineers and physicists working on summability theory
  • Written by the winner of the Dr. Radhakrishnan Award for the Best Teacher in Mathematics
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  • ISBN 978-981-10-4205-8
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Hardcover $109.99
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Softcover $109.99
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  • ISBN 978-981-13-5077-1
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About this book

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..

About the authors

P.N. NATARAJAN, formerly with the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, India, has been an independent researcher and mathematician since his retirement in 2004. He did his Ph.D. at the University of Madras, under Prof. M.S. Rangachari, former director and head of the Ramanujan Institute for Advanced Study in Mathematics, University of Madras. An active researcher, Prof. Natarajan has published over 100 research papers in several international journals like the Proceedings of the American Mathematical SocietyBulletin of the London Mathematical SocietyIndagationes MathematicaeAnnales Mathematiques Blaise Pascal, and Commentationes Mathematicae (Prace Matematyczne). His research interests include summability theory and functional analysis (both classical and ultrametric). Professor Natarajan was honored with the Dr. Radhakrishnan Award for the Best Teacher in Mathematics for the year 1990–91 by the Government of Tamil Nadu. In addition to being invited to visit several renowned institutes in Canada, France, Holland and Greece Prof. Natarajan has participated in several international conferences and chaired sessions. He has authored two books, An Introduction to Ultrametric Summability Theory and its second edition, both published with Springer in 2013 and 2015, respectively.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-981-10-4205-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-981-10-4204-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-981-13-5077-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Classical Summability Theory
Authors
Copyright
2017
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-10-4205-8
DOI
10.1007/978-981-10-4205-8
Hardcover ISBN
978-981-10-4204-1
Softcover ISBN
978-981-13-5077-1
Edition Number
1
Number of Pages
XI, 130
Topics