An Introduction to Ultrametric Summability Theory (eBook, PDF) - Natarajan, P.N.
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This is the second, completely revised and expanded edition of the author’s first book, covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents a brief survey of the research to date in ultrametric summability theory, which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will…mehr

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Produktbeschreibung
This is the second, completely revised and expanded edition of the author’s first book, covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents a brief survey of the research to date in ultrametric summability theory, which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis. The book is also useful as a text for those who wish to specialize in ultrametric summability theory.
Autorenporträt
Pinnangudi Narayanasubramanian Natarajan is former professor and head, Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai. He did his PhD from the University of Madras, under Prof. M.S. Rangachari, former director and head, The Ramanujan Institute for Advanced Study in Mathematics, University of Madras. An active researcher, Prof. Natarajan has over 100 research papers to his credit published in several international journals like Proceedings of the American Mathematical Society, Bulletin of the London Mathematical Society, Indagationes Mathematicae, Annales Mathematiques Blaise Pascal and Commentationes Mathematicae (Prace Matematyczne). His research interest includes 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. Besides visiting several institutes of repute in Canada, France, Holland and Greece on invitation, Prof. Natarajan has participated in several international conferences and chaired sessions, too.

Rezensionen
Most of the material discussed in the book An Introduction to Ultrametric Summability Theory has not appeared in a book form before. The Silverman Toeplitz theorem in an ultra-metric field turns into the following form: an infinite matrix or a summability matrix A = ( a nk ) preserves convergent sequences if and only if sup n ; k a nk < Yen ; lim n ® Yen a nk = d k exists, k = 0, 1, 2, and lim n ® Yen exists. The theorem is proved by using the sliding-hump method avoiding traditional tools like the signum function. Schur s theorem, Steinhaus theorem, and Knopp s core theorem are discussed. It is proved that neither certain Steinhaus type theorems nor the Mazur Orlicz theorem and Brudno s theorem holds. Certain special summability methods, such as the Norlund method, weighted mean method, Euler method, Taylor method and their properties are extensively discussed. Some product theorems and Tauberian theorems are also proved. Double sequences and double series are discussed, and the Silverman Toeplitz theorem for four-dimensional infinite matrices is given. Some applications of this theorem are also discussed in the book. ( Hüseyin Çakalli, Maltepe University, Istanbul, Turkey ) - See more at: