An Introduction to Ultrametric Summability Theory
Description
This is a 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. Three entirely new chapters explore sequence spaces and summability matrices. 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.
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Pinnangudi Narayanasubramanian Natarajan is former Professor and Head, now Professor Emeritus, 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, Dr. Natarajan has more than 150 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 Mat ) and Filomat. 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.
Content
Chapter 1 Introduction and Preliminaries.- Chapter 2 Some Arithmetic and Analysis in ????;Derivatives in Ultrametric Analysis.- Chapter 3 Ultrametric Functional Analysis.- Chapter 4 Ultrametric Summability Theory.- Chapter 5 The N??¨rlund and The Weighted Mean Methods.- Chapter 6 The Euler and The Taylor Methods.- Chapter 7 Tauberian Theorems.- Chapter 8 A Study of Sequence Spaces ????(??) over Ultrametricc Fields.- Chapter 9 On the Sequence Spaces ??(??), ????(??), ??(??), ??(??) over Ultrametric fields.- Chapter 10 A Characterization of the Matrix Class (??, ????) and Summability Matrices of Type ?? in Ultrametric Analysis.- Chapter11 Silverman-Toeplitz Theorem for Double Sequence and Double Series.- Chapter 12 The N??¨rlund Method and The Weighted Mean Method for Dual Sequences.