An Introduction to Ultrametric Summability Theory
Title | An Introduction to Ultrametric Summability Theory PDF eBook |
Author | P. N. Natarajan |
Publisher | |
Pages | 114 |
Release | 2013-11-30 |
Genre | |
ISBN | 9788132216483 |
An Introduction to Ultrametric Summability Theory
Title | An Introduction to Ultrametric Summability Theory PDF eBook |
Author | P.N. Natarajan |
Publisher | Springer Science & Business Media |
Pages | 111 |
Release | 2013-10-18 |
Genre | Mathematics |
ISBN | 8132216474 |
Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents, for the first time, 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.
Classical Summability Theory
Title | Classical Summability Theory PDF eBook |
Author | P.N. Natarajan |
Publisher | Springer |
Pages | 139 |
Release | 2017-04-25 |
Genre | Mathematics |
ISBN | 9811042055 |
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..
Sequence Spaces and Summability over Valued Fields
Title | Sequence Spaces and Summability over Valued Fields PDF eBook |
Author | P. N. Natarajan |
Publisher | CRC Press |
Pages | 217 |
Release | 2019-07-09 |
Genre | Mathematics |
ISBN | 1000065413 |
Sequence spaces and summability over valued fields is a research book aimed at research scholars, graduate students and teachers with an interest in Summability Theory both Classical (Archimedean) and Ultrametric (non-Archimedean). The book presents theory and methods in the chosen topic, spread over 8 chapters that seem to be important at research level in a still developing topic. Key Features Presented in a self-contained manner Provides examples and counterexamples in the relevant contexts Provides extensive references at the end of each chapter to enable the reader to do further research in the topic Presented in the same book, a comparative study of Archimedean and non-Archimedean Summability Theory Appeals to young researchers and experienced mathematicians who wish to explore new areas in Summability Theory The book is written by a very experienced educator and researcher in Mathematical Analysis particularly Summability Theory.
Advanced Topics in Mathematical Analysis
Title | Advanced Topics in Mathematical Analysis PDF eBook |
Author | Michael Ruzhansky |
Publisher | CRC Press |
Pages | 428 |
Release | 2019-01-08 |
Genre | Mathematics |
ISBN | 1351142100 |
Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.
An Introductory Course in Summability Theory
Title | An Introductory Course in Summability Theory PDF eBook |
Author | Ants Aasma |
Publisher | |
Pages | 201 |
Release | 2017 |
Genre | MATHEMATICS |
ISBN | 9781119397786 |
Summability Theory And Its Applications
Title | Summability Theory And Its Applications PDF eBook |
Author | Feyzi Basar |
Publisher | Bentham Science Publishers |
Pages | 410 |
Release | 2012-09-07 |
Genre | Mathematics |
ISBN | 1608052524 |
The theory of summability has many uses throughout analysis and applied mathematics. Engineers and physicists working with Fourier series or analytic continuation will also find the concepts of summability theory valuable to their research. The concepts of summability have been extended to the sequences of fuzzy numbers and also to the theorems of ergodic theory. This ebook explains various aspects of summability and demonstrates applications in a coherent manner. The content can readily serve as a useful series of lecture notes on the subject. This ebook comprises of 8 chapters starting from classical sequence spaces and covering matrix transformations and fuzzy numbers. An accompanying bibliography with extensive references makes this a valuable source of information for readers interested in summability theory as well as other branches of science.