An Introduction to Ultrametric Summability Theory

by P.N. Natarajan

Overview

This book presents an overview of the research in ultrametric summability theory. It will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis.

Product Details

ISBN-13:	9788132216476
Publisher:	Springer-Verlag New York, LLC
Publication date:	10/18/2013
Series:	SpringerBriefs in Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	102
File size:	4 MB

About the Author

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.

Table of Contents

1. Introduction and Preliminaries.- 2. Some Arithmetic and Analysis in Qp; Derivatives in Ultrametric Analysis.- 3. Ultrametric Functional Analysis.- 4. Ultrametric Summability Theory.- 5. The Nörlund and the Weighted Mean Methods.- 6. The Euler and the Taylor Methods.- 7. Tauberian Theorems.- 8. Silverman-Toeplitz Theorem for Double Sequences and Double Series.- 9. The Nörlund Method and the Weighted Mean Method for Double Sequences.