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Classical Summability Theory
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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..
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.
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.
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.
Book Synopsis Classical Fourier Analysis by : Loukas Grafakos
Download or read book Classical Fourier Analysis written by Loukas Grafakos and published by Springer Science & Business Media. This book was released on 2008-09-18 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). From a review of the first edition: “Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online
Book Synopsis Classical and Discrete Functional Analysis with Measure Theory by : Martin Buntinas
Download or read book Classical and Discrete Functional Analysis with Measure Theory written by Martin Buntinas and published by Cambridge University Press. This book was released on 2022-01-20 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced undergraduate/beginning graduate text covers measure theory and discrete aspects of functional analysis, with 760 exercises.
Book Synopsis An Introductory Course in Summability Theory by : Ants Aasma
Download or read book An Introductory Course in Summability Theory written by Ants Aasma and published by John Wiley & Sons. This book was released on 2017-04-05 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
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.
Book Synopsis Asymptotics and Borel Summability by : Ovidiu Costin
Download or read book Asymptotics and Borel Summability written by Ovidiu Costin and published by CRC Press. This book was released on 2008-12-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr
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 155 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.
Book Synopsis Summability Calculus by : Ibrahim M. Alabdulmohsin
Download or read book Summability Calculus written by Ibrahim M. Alabdulmohsin and published by Springer. This book was released on 2018-03-07 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.
Book Synopsis Probability Theory with Applications by : Malempati M. Rao
Download or read book Probability Theory with Applications written by Malempati M. Rao and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a revised and expanded edition of a successful graduate and reference text. The book is designed for a standard graduate course on probability theory, including some important applications. The new edition offers a detailed treatment of the core area of probability, and both structural and limit results are presented in detail. Compared to the first edition, the material and presentation are better highlighted; each chapter is improved and updated.
Book Synopsis Ramanujan Summation of Divergent Series by : Bernard Candelpergher
Download or read book Ramanujan Summation of Divergent Series written by Bernard Candelpergher and published by Springer. This book was released on 2017-09-12 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.
Book Synopsis Asymptotic Expansions and Summability by : Pascal Remy
Download or read book Asymptotic Expansions and Summability written by Pascal Remy and published by Springer Nature. This book was released on with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis 2nd International Students Science Congress Proceedings by : Mahamat Ali Amine Ouchar
Download or read book 2nd International Students Science Congress Proceedings written by Mahamat Ali Amine Ouchar and published by Infinite Study. This book was released on with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this study is to determine PstI polymorphism in the exon 6 region of the Pituitary-specific Transcription Factor (Pit-1) gene which is regarded as a candidate gene in mammals in regulating growth and development in 6 different goat breeds reared in Turkey. PstI polymorphism in Pit-1 gene (450 bp) was investigated by Restriction Fragment Length Polymorphism (RFLP) method in a total of 217 goats including 36 Hair, 18 Angora, 43 Kilis, 37 Honamlı, 46 Halep and 37 heads of Saanen breeds.
