P.N. Natarajan's Books

An Introductory Course in Summability Theory

By: Ants Aasma,Hemen Dutta,P. N. Natarajan

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An Introductory Course in Summability Theory

By: Ants Aasma,Hemen Dutta,P. N. Natarajan

An introductory course in summability theory for students, researchers, physicists, and engineers In creating this book, the authors’ intent was to provide graduate students, researchers, physicists, and engineers with a reasonable introduction to summability theory. Over the course of nine chapters, the authors cover all of the fundamental concepts and equations informing summability theory and its applications, as well as some of its lesser known aspects. Following a brief introduction to the history of summability theory, general matrix methods are introduced, and the Silverman-Toeplitz theorem on regular matrices is discussed. A variety of special summability methods, including the Nörlund method, the Weighted Mean method, the Abel method, and the (C, 1) - method are next examined. An entire chapter is devoted to a discussion of some elementary Tauberian theorems involving certain summability methods. Following this are chapters devoted to matrix transforms of summability and absolute summability domains of reversible and normal methods; the notion of a perfect matrix method; matrix transforms of summability and absolute summability domains of the Cesàro and Riesz methods; convergence and the boundedness of sequences with speed; and convergence, boundedness, and summability with speed. • Discusses results on matrix transforms of several matrix methods • The only English-language textbook describing the notions of convergence, boundedness, and summability with speed, as well as their applications in approximation theory • Compares the approximation orders of Fourier expansions in Banach spaces by different matrix methods • Matrix transforms of summability domains of regular perfect matrix methods are examined • Each chapter contains several solved examples and end-of-chapter exercises, including hints for solutions An Introductory Course in Summability Theory is the ideal first text in summability theory for graduate students, especially those having a good grasp of real and complex analysis. It is also a valuable reference for mathematics researchers and for physicists and engineers who work with Fourier series, Fourier transforms, or analytic continuation. ANTS AASMA, PhD, is Associate Professor of Mathematical Economics in the Department of Economics and Finance at Tallinn University of Technology, Estonia. HEMEN DUTTA, PhD, is Senior Assistant Professor of Mathematics at Gauhati University, India. P.N. NATARAJAN, PhD, is Formerly Professor and Head of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India.

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355

Publisher

John Wiley & Sons

Published Date

ISBN 10

1119397774

ISBN 13

9781119397779

Concise Introduction to Basic Real Analysis

By: Hemen Dutta,P. N. Natarajan,Yeol Je Cho

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Concise Introduction to Basic Real Analysis

By: Hemen Dutta,P. N. Natarajan,Yeol Je Cho

This book provides an introduction to basic topics in Real Analysis and makes the subject easily understandable to all learners. The book is useful for those that are involved with Real Analysis in disciplines such as mathematics, engineering, technology, and other physical sciences. It provides a good balance while dealing with the basic and essential topics that enable the reader to learn the more advanced topics easily. It includes many examples and end of chapter exercises including hints for solutions in several critical cases. The book is ideal for students, instructors, as well as those doing research in areas requiring a basic knowledge of Real Analysis. Those more advanced in the field will also find the book useful to refresh their knowledge of the topic. Features Includes basic and essential topics of real analysis Adopts a reasonable approach to make the subject easier to learn Contains many solved examples and exercise at the end of each chapter Presents a quick review of the fundamentals of set theory Covers the real number system Discusses the basic concepts of metric spaces and complete metric spaces

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Page Count

251

Publisher

CRC Press

Published Date

ISBN 10

0429876335

ISBN 13

9780429876332

Functional Analysis and Summability

By: P.N. Natarajan

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Functional Analysis and Summability

By: P.N. Natarajan

There are excellent books on both functional analysis and summability. Most of them are very terse. In Functional Analysis and Summability, the author makes a sincere attempt for a gentle introduction of these topics to students. In the functional analysis component of the book, the Hahn–Banach theorem, Banach–Steinhaus theorem (or uniform boundedness principle), the open mapping theorem, the closed graph theorem, and the Riesz representation theorem are highlighted. In the summability component of the book, the Silverman–Toeplitz theorem, Schur’s theorem, the Steinhaus theorem, and the Steinhaus-type theorems are proved. The utility of functional analytic tools like the uniform boundedness principle to prove some results in summability theory is also pointed out. Features A gentle introduction of the topics to the students is attempted. Basic results of functional analysis and summability theory and their applications are highlighted. Many examples are provided in the text. Each chapter ends with useful exercises. This book will be useful to postgraduate students, pre-research level students, and research scholars in mathematics. Students of physics and engineering will also find this book useful since topics in the book also have applications in related areas.

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Page Count

220

Publisher

CRC Press

Published Date

ISBN 10

1000191478

ISBN 13

9781000191479

Sequence Spaces and Summability over Valued Fields

By: P. N. Natarajan

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Sequence Spaces and Summability over Valued Fields

By: P. N. Natarajan

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.

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Page Count

217

Publisher

CRC Press

Published Date

ISBN 10

1000065413

ISBN 13

9781000065411

An Introduction to Ultrametric Summability Theory

By: P.N. Natarajan

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An Introduction to Ultrametric Summability Theory

By: P.N. Natarajan

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.

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111

Publisher

Springer Science & Business Media

Published Date

ISBN 10

8132216474

ISBN 13

9788132216476

Classical Summability Theory

By: P.N. Natarajan

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Classical Summability Theory

By: P.N. Natarajan

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..

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Page Count

139

Publisher

Springer

Published Date

ISBN 10

9811042055

ISBN 13

9789811042058

Economics of Fisheries

Ecology and Fisheries of Oxbow Lakes

By: P. N. Panday,B. K. Gorai,B. C. Jha

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Economics of Fisheries

Ecology and Fisheries of Oxbow Lakes

By: P. N. Panday,B. K. Gorai,B. C. Jha

Highlights the presentstate-of-art of ecology, biodiversity and fisheries of oxbow lakes of Bihar,which hitherto remain neglected till date. It also contains guidelines for theholistic management of fisheries and conservation of the biodiversity of theregion.

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Page Count

208

Publisher

APH Publishing

Published Date

ISBN 10

8176488585

ISBN 13

9788176488587

Silk Worm Crops

By: D. Chakravorty,P.N. Pandey

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Silk Worm Crops

By: D. Chakravorty,P.N. Pandey

Study conducted at Maharashtra State, India.

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240

Publisher

APH Publishing

Published Date

ISBN 10

8176488917

ISBN 13

9788176488914

The Encyclopedia of Herbs and Spices

By: P N Ravindran

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The Encyclopedia of Herbs and Spices

By: P N Ravindran

The Encyclopedia of Herbs and Spices provides comprehensive coverage of the taxonomy, botany, chemistry, functional properties, medicinal uses, culinary uses and safety issues relating to over 250 species of herbs and spices. These herbs and spices constitute an important agricultural commodity; many are traded globally and are indispensable for pharmaceuticals, flavouring foods and beverages, and in the perfumery and cosmetic industries. More recently, they are increasingly being identified as having high nutraceutical potential and important value in human healthcare. This encyclopedia is an excellent resource for researchers, students, growers and manufacturers, in the fields of horticulture, agriculture, botany, crop sciences, food science and pharmacognosy.

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1178

Publisher

CABI

Published Date

ISBN 10

1780643152

ISBN 13

9781780643151

Classical Summability Theory

By: P.N. Natarajan

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Classical Summability Theory

By: P.N. Natarajan

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Page Count

139

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Springer

Published Date

ISBN 10

9811042055

ISBN 13

9789811042058

An Introduction to Ultrametric Summability Theory

By: P.N. Natarajan

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An Introduction to Ultrametric Summability Theory

By: P.N. Natarajan

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.

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Page Count

169

Publisher

Springer

Published Date

ISBN 10

8132225597

ISBN 13

9788132225591

Sequence Spaces and Summability over Valued Fields

By: P. N. Natarajan

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Sequence Spaces and Summability over Valued Fields

By: P. N. Natarajan

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Page Count

217

Publisher

CRC Press

Published Date

ISBN 10

1000065413

ISBN 13

9781000065411

An Introductory Course in Summability Theory

By: Ants Aasma,Hemen Dutta,P. N. Natarajan

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An Introductory Course in Summability Theory

By: Ants Aasma,Hemen Dutta,P. N. Natarajan

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216

Publisher

John Wiley & Sons

Published Date

ISBN 10

1119397693

ISBN 13

9781119397694

Concise Introduction to Basic Real Analysis

By: Hemen Dutta,P. N. Natarajan,Yeol Je Cho

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Concise Introduction to Basic Real Analysis

By: Hemen Dutta,P. N. Natarajan,Yeol Je Cho

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Solve jigsaw puzzle

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251

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CRC Press

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ISBN 10

0429876335

ISBN 13

9780429876332

Book's by P.N. Natarajan

An Introductory Course in Summability Theory

An Introductory Course in Summability Theory

Concise Introduction to Basic Real Analysis

Concise Introduction to Basic Real Analysis

Functional Analysis and Summability

Functional Analysis and Summability

Sequence Spaces and Summability over Valued Fields

Sequence Spaces and Summability over Valued Fields

An Introduction to Ultrametric Summability Theory

An Introduction to Ultrametric Summability Theory

Classical Summability Theory

Classical Summability Theory

Economics of Fisheries

Economics of Fisheries

Silk Worm Crops

Silk Worm Crops

The Encyclopedia of Herbs and Spices

The Encyclopedia of Herbs and Spices

Classical Summability Theory

Classical Summability Theory

An Introduction to Ultrametric Summability Theory

An Introduction to Ultrametric Summability Theory

Sequence Spaces and Summability over Valued Fields

Sequence Spaces and Summability over Valued Fields

An Introductory Course in Summability Theory

An Introductory Course in Summability Theory

Concise Introduction to Basic Real Analysis

Concise Introduction to Basic Real Analysis

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