Some Applications Of Functional Analysis To Summability Theory

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Functional Analysis and Summability

Author : P.N. Natarajan
Publisher : CRC Press
ISBN 13 : 1000191494
Total Pages : 155 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 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.

Introductory Functional Analysis with Applications

Author : Erwin Kreyszig
Publisher : John Wiley & Sons
ISBN 13 : 0471504599
Total Pages : 706 pages
Book Rating : 4.4/5 (715 download)

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Book Synopsis Introductory Functional Analysis with Applications by : Erwin Kreyszig

Download or read book Introductory Functional Analysis with Applications written by Erwin Kreyszig and published by John Wiley & Sons. This book was released on 1991-01-16 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter Henrici Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel Topics in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel Topics In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry

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.

Elementary Functional Analysis

Author : Georgi E. Shilov
Publisher : Courier Corporation
ISBN 13 : 0486318680
Total Pages : 354 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Elementary Functional Analysis by : Georgi E. Shilov

Download or read book Elementary Functional Analysis written by Georgi E. Shilov and published by Courier Corporation. This book was released on 2013-04-15 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 edition.

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.

Some Applications of Functional Analysis in Mathematical Physics

Author : S. L. Sobolev
Publisher : American Mathematical Soc.
ISBN 13 : 9780821898321
Total Pages : 300 pages
Book Rating : 4.8/5 (983 download)

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Book Synopsis Some Applications of Functional Analysis in Mathematical Physics by : S. L. Sobolev

Download or read book Some Applications of Functional Analysis in Mathematical Physics written by S. L. Sobolev and published by American Mathematical Soc.. This book was released on 2008-04-14 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special problems of functional analysis Variational methods in mathematical physics The theory of hyperbolic partial differential equations Comments Appendix: Methode nouvelle a resoudre le probleme de Cauchy pour les equations lineaires hyperboliques normales Comments on the appendix Bibliography Index

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 and Discrete Functional Analysis with Measure Theory

Author : Martin Buntinas
Publisher : Cambridge University Press
ISBN 13 : 1107034140
Total Pages : 471 pages
Book Rating : 4.1/5 (7 download)

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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.

Saks Spaces and Applications to Functional Analysis

Author : J.B. Cooper
Publisher : Elsevier
ISBN 13 : 0080872506
Total Pages : 383 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Saks Spaces and Applications to Functional Analysis by : J.B. Cooper

Download or read book Saks Spaces and Applications to Functional Analysis written by J.B. Cooper and published by Elsevier. This book was released on 2011-08-18 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this monograph appeared in 1978. In view of the progress made in the intervening years, the original text has been revised, several new sections have been added and the list of references has been updated. The book presents a systematic treatment of the theory of Saks Spaces, i.e. vector space with a norm and related, subsidiary locally convex topology. Applications are given to space of bounded, continuous functions, to measure theory, vector measures, spaces of bounded measurable functions, spaces of bounded analytic functions, and to W*-algebras.

Elementary Functional Analysis

Author : Charles W Swartz
Publisher : World Scientific Publishing Company
ISBN 13 : 9813107529
Total Pages : 192 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Elementary Functional Analysis by : Charles W Swartz

Download or read book Elementary Functional Analysis written by Charles W Swartz and published by World Scientific Publishing Company. This book was released on 2009-07-13 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.

Mathematical Analysis and Its Applications

Author : S. M. Mazhar
Publisher : Elsevier
ISBN 13 : 1483148114
Total Pages : 443 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Mathematical Analysis and Its Applications by : S. M. Mazhar

Download or read book Mathematical Analysis and Its Applications written by S. M. Mazhar and published by Elsevier. This book was released on 2014-05-17 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis and its Applications covers the proceedings of the International Conference on Mathematical Analysis and its Applications. The book presents studies that discuss several mathematical analysis methods and their respective applications. The text presents 38 papers that discuss topics, such as approximation of continuous functions by ultraspherical series and classes of bi-univalent functions. The representation of multipliers of eigen and joint function expansions of nonlocal spectral problems for first- and second-order differential operators is also discussed. The book will be of great interest to researchers and professionals whose work involves the use of mathematical analysis.

An Introduction to Ultrametric Summability Theory

Author : P.N. Natarajan
Publisher :
ISBN 13 : 9788132225607
Total Pages : pages
Book Rating : 4.2/5 (256 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 . 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.

Linear Functional Analysis

Author : Peng Yee Lee
Publisher : World Scientific
ISBN 13 : 9814505854
Total Pages : 266 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Linear Functional Analysis by : Peng Yee Lee

Download or read book Linear Functional Analysis written by Peng Yee Lee and published by World Scientific. This book was released on 1992-06-19 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: With an addendum by Wu Congxin (Harbin Institute of Technology)Linear Functional Analysis resulted from a series of lectures Orlicz gave in Beijing, China, 1958. The orignal edition was published in Chinese in 1963. It contains all the major theorems that would normally appear in a modern text, the results of special interest to the Polish school, and others which are not easily available elsewhere. Orlicz provided in this book some rare insight and motivation in the subject which was initiated by the Polish school. An addendum to some recent results in Orlicz spaces is included.

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.

Nonlinear Functional Analysis

Author : Jacob T. Schwartz
Publisher : CRC Press
ISBN 13 : 9780677015002
Total Pages : 248 pages
Book Rating : 4.0/5 (15 download)

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Book Synopsis Nonlinear Functional Analysis by : Jacob T. Schwartz

Download or read book Nonlinear Functional Analysis written by Jacob T. Schwartz and published by CRC Press. This book was released on 1969 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1021 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1021 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

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.