Overview

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.

Full Product Details

Author:   P.N. Natarajan
Publisher:   Springer, India, Private Ltd
Imprint:   Springer, India, Private Ltd
Edition:   Third Edition 2026
ISBN:  

9788132240228

ISBN 10:   8132240227
Publication Date:   31 May 2026
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Forthcoming
Availability:   Not yet available  
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Table of Contents

Chapter 1 Introduction and Preliminaries.- Chapter 2 Some Arithmetic and Analysis in 𝑸𝒑;Derivatives in Ultrametric Analysis.- Chapter 3 Ultrametric Functional Analysis.- Chapter 4 Ultrametric Summability Theory.- Chapter 5 The N𝒐̈rlund and The Weighted Mean Methods.- Chapter 6 The Euler and The Taylor Methods.- Chapter 7 Tauberian Theorems.- Chapter 8 A Study of Sequence Spaces 𝑪𝟎(𝒑) over Ultrametricc Fields.- Chapter 9 On the Sequence Spaces 𝒍(𝒑), 𝒄𝟎(𝒑), 𝒄(𝒑), 𝒍(𝒑) over Ultrametric fields.- Chapter 10 A Characterization of the Matrix Class (𝒍, 𝒄𝒐) and Summability Matrices of Type 𝑴 in Ultrametric Analysis.- Chapter11 Silverman-Toeplitz Theorem for Double Sequence and Double Series.- Chapter 12 The N𝒐̈rlund Method and The Weighted Mean Method for Dual Sequences.

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Author Information

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.

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