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Summability Through Functional Analysis

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Summability Through Functional Analysis

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Author : A. Wilansky
language : en
Publisher: Elsevier
Release Date : 2000-04-01

Summability Through Functional Analysis written by A. Wilansky and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.

Summability is an extremely fruitful area for the application of functional analysis; this volume could be used as a source for such applications. Those parts of summability which only have ``hard'' (classical) proofs are omitted; the theorems given all have ``soft'' (functional analytic) proofs.

Summability Through Functional Analysis

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Author : Albert Wilansky
language : en
Publisher: North Holland
Release Date : 1984-01-01

Summability Through Functional Analysis written by Albert Wilansky and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.

Functional Analysis And Summability

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Author : P.N. Natarajan
language : en
Publisher: CRC Press
Release Date : 2020-09-07

Functional Analysis And Summability written by P.N. Natarajan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-07 with Mathematics categories.

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.

Summability Fixed Point Theory And Generalized Integrals With Applications

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Author : Hemanta Kalita
language : en
Publisher: CRC Press
Release Date : 2025-06-19

Summability Fixed Point Theory And Generalized Integrals With Applications written by Hemanta Kalita and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.

This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results of double sequence spaces as the four-dimensional forward difference matrix in double sequence spaces, several new fixed point on Hadamard type fractional integral and differential operator related to the qualitative properties of solutions like, existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. It also includes several new areas of nonabsolute integration theory are introduced and their applications to other fields. This reference text is for researchers, academics, and professionals in the field of pure and applied mathematics. Covers recent research breakthroughs in this field offering new approaches and methods for both theoretical exploration and practical application Presents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applications Highlights fixed-point theory’s application to real-world problems and offers solutions to various complex challenges Introduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integral Discusses sequence spaces and functional analysis, including the exploration of double sequence spaces and the four-dimensional forward difference matrix, offering valuable contributions to ongoing research

An Introductory Course In Summability Theory

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Author : Ants Aasma
language : en
Publisher: John Wiley & Sons
Release Date : 2017-04-05

An Introductory Course In Summability Theory written by Ants Aasma and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-05 with Mathematics categories.

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.

Classical And Modern Methods In Summability

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Author : Johann Boos
language : en
Publisher: Clarendon Press
Release Date : 2000

Classical And Modern Methods In Summability written by Johann Boos and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

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.

Functional Analysis And Theory Of Summability

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Author : Ülo Lepik
language : en
Publisher:
Release Date : 1993

Functional Analysis And Theory Of Summability written by Ülo Lepik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Functional analysis categories.

Classical And Discrete Functional Analysis With Measure Theory

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Author : Martin Buntinas
language : en
Publisher: Cambridge University Press
Release Date : 2022-01-20

Classical And Discrete Functional Analysis With Measure Theory written by Martin Buntinas and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-20 with Mathematics categories.

This advanced undergraduate/beginning graduate text covers measure theory and discrete aspects of functional analysis, with 760 exercises.

Summability Theory And Its Applications

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Author : Feyzi Başar
language : en
Publisher: CRC Press
Release Date : 2022-06-27

Summability Theory And Its Applications written by Feyzi Başar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-27 with Mathematics categories.

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.

An Introduction To Ultrametric Summability Theory

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Author : P.N. Natarajan
language : en
Publisher: Springer
Release Date : 2015-09-08

An Introduction To Ultrametric Summability Theory written by P.N. Natarajan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-08 with Mathematics categories.

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.

Summability Through Functional Analysis

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