Sequence Spaces And Summability Over Valued Fields

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Sequence Spaces and Summability over Valued Fields

Author : P. N. Natarajan
Publisher : CRC Press
ISBN 13 : 1000065413
Total Pages : 217 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Sequence Spaces and Summability over Valued Fields by : P. N. Natarajan

Download or read book Sequence Spaces and Summability over Valued Fields written by P. N. Natarajan and published by CRC Press. This book was released on 2019-07-09 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Sequence Spaces and Summability over Valued Fields

Author : P. N. Natarajan
Publisher : CRC Press
ISBN 13 : 1000074919
Total Pages : 169 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Sequence Spaces and Summability over Valued Fields by : P. N. Natarajan

Download or read book Sequence Spaces and Summability over Valued Fields written by P. N. Natarajan and published by CRC Press. This book was released on 2019-07-09 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Ultrametric Summability Theory

Author : P.N. Natarajan
Publisher : Springer Science & Business Media
ISBN 13 : 8132216474
Total Pages : 111 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis An Introduction to Ultrametric Summability Theory by : P.N. Natarajan

Download or read book An Introduction to Ultrametric Summability Theory written by P.N. Natarajan and published by Springer Science & Business Media. This book was released on 2013-10-18 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Functional Analysis and Summability

Author : P.N. Natarajan
Publisher : CRC Press
ISBN 13 : 1000191494
Total Pages : 194 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Functional Analysis and Summability by : P.N. Natarajan

Download or read book Functional Analysis and Summability written by P.N. Natarajan and published by CRC Press. This book was released on 2020-09-08 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Sequences, Summability and Fourier Analysis

Author : S. Nanda
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9788173196027
Total Pages : 234 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis Sequences, Summability and Fourier Analysis by : S. Nanda

Download or read book Sequences, Summability and Fourier Analysis written by S. Nanda and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequences, Summability and Fourier Analysis deals with various aspects of summability, a major branch of analysis. The subject grew extensively during the twentieth century through the contribution of eminent analysts, but there are numerous unsolved problems, which still baffle the present-day scholars, as the application side has been poorly attended to. This volume contains original research articles, many valuable survey articles on approximation theory, multivalent functions, almost convergence and absolute almost convergence, Tauberian theorems, Köthe-Toeplitz duals of sequence spaces, random Fourier series, stochastic integrals, interpolative subspaces of Banach space, metric transformations in sequence spaces, absolute summability and Nörlund summability.

Current Topics in Summability Theory and Applications

Author : Hemen Dutta
Publisher : Springer
ISBN 13 : 9811009139
Total Pages : 436 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Current Topics in Summability Theory and Applications by : Hemen Dutta

Download or read book Current Topics in Summability Theory and Applications written by Hemen Dutta and published by Springer. This book was released on 2016-04-28 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses recent developments in and contemporary research on summability theory, including general summability methods, direct theorems on summability, absolute and strong summability, special methods of summability, functional analytic methods in summability, and related topics and applications. All contributing authors are eminent scientists, researchers and scholars in their respective fields, and hail from around the world. The book can be used as a textbook for graduate and senior undergraduate students, and as a valuable reference guide for researchers and practitioners in the fields of summability theory and functional analysis. Summability theory is generally used in analysis and applied mathematics. It plays an important part in the engineering sciences, and various aspects of the theory have long since been studied by researchers all over the world.

Sequence Spaces

Author : Mohammad Mursaleen
Publisher : CRC Press
ISBN 13 : 1000045153
Total Pages : 313 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Sequence Spaces by : Mohammad Mursaleen

Download or read book Sequence Spaces written by Mohammad Mursaleen and published by CRC Press. This book was released on 2020-03-10 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at both experts and non-experts with an interest in getting acquainted with sequence spaces, matrix transformations and their applications. It consists of several new results which are part of the recent research on these topics. It provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more. This book presents the important role sequences and series play in everyday life, it covers geometry of Banach Sequence Spaces, it discusses the importance of generalized limit, it offers spectrum and fine spectrum of several linear operators and includes fuzzy valued sequences which exhibits the study of sequence spaces in fuzzy settings. This book is the main attraction for those who work in Sequence Spaces, Summability Theory and would also serve as a good source of reference for those involved with any topic of Real or Functional Analysis.

Classical Summability Theory

Author : P.N. Natarajan
Publisher : Springer
ISBN 13 : 9811042055
Total Pages : 139 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Classical Summability Theory by : P.N. Natarajan

Download or read book Classical Summability Theory written by P.N. Natarajan and published by Springer. This book was released on 2017-04-25 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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..

Advanced Topics in Mathematical Analysis

Author : Michael Ruzhansky
Publisher : CRC Press
ISBN 13 : 1351142100
Total Pages : 428 pages
Book Rating : 4.3/5 (511 download)

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Book Synopsis Advanced Topics in Mathematical Analysis by : Michael Ruzhansky

Download or read book Advanced Topics in Mathematical Analysis written by Michael Ruzhansky and published by CRC Press. This book was released on 2019-01-08 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Sequence Spaces

Author : Mohammad Mursaleen
Publisher : CRC Press
ISBN 13 : 100004517X
Total Pages : 267 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Sequence Spaces by : Mohammad Mursaleen

Download or read book Sequence Spaces written by Mohammad Mursaleen and published by CRC Press. This book was released on 2020-03-10 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at both experts and non-experts with an interest in getting acquainted with sequence spaces, matrix transformations and their applications. It consists of several new results which are part of the recent research on these topics. It provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more. This book presents the important role sequences and series play in everyday life, it covers geometry of Banach Sequence Spaces, it discusses the importance of generalized limit, it offers spectrum and fine spectrum of several linear operators and includes fuzzy valued sequences which exhibits the study of sequence spaces in fuzzy settings. This book is the main attraction for those who work in Sequence Spaces, Summability Theory and would also serve as a good source of reference for those involved with any topic of Real or Functional Analysis.

Summability Theory and Its Applications

Author : Feyzi Başar
Publisher : CRC Press
ISBN 13 : 1000599140
Total Pages : 521 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Summability Theory and Its Applications by : Feyzi Başar

Download or read book Summability Theory and Its Applications written by Feyzi Başar and published by CRC Press. This book was released on 2022-06-27 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summability Theory and Its Applications explains various aspects of summability and demonstrates its applications in a rigorous and coherent manner. The content can readily serve as a reference or as a useful series of lecture notes on the subject. This substantially revised new edition includes brand new material across several chapters as well as several corrections, including: the addition of the domain of Cesaro matrix C(m) of order m in the classical sequence spaces to Chapter 4; and introducing the domain of four-dimensional binomial matrix in the spaces of bounded, convergent in the Pringsheim's sense, both convergent in the Pringsheim's sense and bounded, and regularly convergent double sequences, in Chapter 7. Features Investigates different types of summable spaces and computes their dual Suitable for graduate students and researchers with a (special) interest in spaces of single and double sequences, matrix transformations and domains of triangle matrices Can serve as a reference or as supplementary reading in a computational physics course, or as a key text for special Analysis seminars.

Convergence Theorems for Lattice Group-Valued Measures

Author : Antonio Boccuto
Publisher : Bentham Science Publishers
ISBN 13 : 1681080095
Total Pages : 548 pages
Book Rating : 4.6/5 (81 download)

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Book Synopsis Convergence Theorems for Lattice Group-Valued Measures by : Antonio Boccuto

Download or read book Convergence Theorems for Lattice Group-Valued Measures written by Antonio Boccuto and published by Bentham Science Publishers. This book was released on 2015-04-06 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convergence Theorems for Lattice Group-valued Measures explains limit and boundedness theorems for measures taking values in abstract structures. The book begins with a historical survey about these topics since the beginning of the last century, moving on to basic notions and preliminaries on filters/ideals, lattice groups, measures and tools which are featured in the rest of this text. Readers will also find a survey on recent classical results about limit, boundedness and extension theorems for lattice group-valued measures followed by information about recent developments on these kinds of theorems and several results in the setting of filter/ideal convergence. In addition, each chapter has a general description of the topics and an appendix on random variables, concepts and lattices is also provided. Thus readers will benefit from this book through an easy-to-read historical survey about all the problems on convergence and boundedness theorems, and the techniques and tools which are used to prove the main results. The book serves as a primer for undergraduate, postgraduate and Ph. D. students on mathematical lattice and topological groups and filters, and a treatise for expert researchers who aim to extend their knowledge base.

Ultrametric Functional Analysis

Author : Wilhelmus Hendricus Schikhof
Publisher : American Mathematical Soc.
ISBN 13 : 0821833200
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Ultrametric Functional Analysis by : Wilhelmus Hendricus Schikhof

Download or read book Ultrametric Functional Analysis written by Wilhelmus Hendricus Schikhof and published by American Mathematical Soc.. This book was released on 2003 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research articles based on lectures given at the Seventh International Conference on $p$-adic Functional Analysis. The articles, written by leading international experts, provide a complete overview of the latest contributions in basic functional analysis (Hilbert and Banach spaces, locally convex spaces, orthogonality, inductive limits, spaces of continuous functions, strict topologies, operator theory, automatic continuity, measure and integrations, Banach and topological algebras, summability methods, and ultrametric spaces), analytic functions (meromorphic functions, roots of rational functions, characterization of injective holomorphic functions, and Gelfand transforms in algebras of analytic functions), differential equations, Banach-Hopf algebras, Cauchy theory of Levi-Civita fields, finite differences, weighted means, $p$-adic dynamical systems, and non-Archimedean probability theory and stochastic processes. The book is written for graduate students and research mathematicians. It also would make a good reference source for those in related areas, such as classical functional analysis, complex analytic functions, probability theory, dynamical systems, orthomodular spaces, number theory, and representations of $p$-adic groups.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 974 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Journal of the Ramanujan Mathematical Society

Author :
Publisher :
ISBN 13 :
Total Pages : 432 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Journal of the Ramanujan Mathematical Society by :

Download or read book Journal of the Ramanujan Mathematical Society written by and published by . This book was released on 1990 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Classical and Modern Methods in Summability

Author : Johann Boos
Publisher : Clarendon Press
ISBN 13 : 9780198501657
Total Pages : 616 pages
Book Rating : 4.5/5 (16 download)

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Book Synopsis Classical and Modern Methods in Summability by : Johann Boos

Download or read book Classical and Modern Methods in Summability written by Johann Boos and published by Clarendon Press. This book was released on 2000 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summability is a mathematical topic with a long tradition and many applications in, for example, function theory, number theory, and stochastics. It was originally based on classical analytical methods, but was strongly influenced by modern functional analytical methods during the last seven decades. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Part I contains a short general introduction to summability, the basic classical theory concerning mainly inclusion theorems and theorems of the Silverman-Toeplitz type, a presentation of the most important classes of summability methods, Tauberian theorems, and applications of matrix methods. The proofs in Part I are exclusively done by applying classical analytical methods. Part II is concerned with modern functional analytical methods in summability, and contains the essential functional analytical basis required in later parts of the book, topologization of sequence spaces as K- and KF-spaces, domains of matrix methods as FK-spaces and their topological structure. In this part the proofs are of functional analytical nature only. Part III of the present book deals with topics in summability and topological sequence spaces which require the combination of classical and modern methods. It covers investigations of the constistency of matrix methods and of the bounded domain of matrix methods via Saks space theory, and the presentation of some aspects in topological sequence spaces. Lecturers, graduate students, and researchers working in summability and related topics will find this book a useful introduction and reference work.

Sequence Space Theory with Applications

Author : S. A. Mohiuddine
Publisher : CRC Press
ISBN 13 : 1000610047
Total Pages : 307 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Sequence Space Theory with Applications by : S. A. Mohiuddine

Download or read book Sequence Space Theory with Applications written by S. A. Mohiuddine and published by CRC Press. This book was released on 2022-07-20 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book features original chapters on sequence spaces involving the idea of ideal convergence, modulus function, multiplier sequences, Riesz mean, Fibonacci difference matrix etc., and illustrate their involvement in various applications. The preliminaries have been presented in the beginning of each chapter and then the advanced discussion takes place, so it is useful for both expert and nonexpert on aforesaid topics. The book consists of original thirteen research chapters contributed by the well-recognized researchers in the field of sequence spaces with associated applications. Features Discusses the Fibonacci and vector valued difference sequence spaces Presents the solution of Volterra integral equation in Banach algebra Discusses some sequence spaces involving invariant mean and related to the domain of Jordan totient matrix Presents the Tauberian theorems of double sequences Discusses the paranormed Riesz difference sequence space of fractional order Includes a technique for studying the existence of solutions of infinite system of functional integro-differential equations in Banach sequence spaces The subject of book is an active area of research of present time internationally and would serve as a good source for researcher and educators involved with the topic of sequence spaces.