{"product_id":"an-introductory-course-in-summability-theory-isbn-9781119397694","title":"An Introductory Course in Summability Theory","description":"\u003cp\u003e\u003cb\u003eAn introductory course in summability theory for students, researchers, physicists, and engineers\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIn 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.\u003c\/p\u003e \u003cp\u003e• Discusses results on matrix transforms of several matrix methods\u003c\/p\u003e \u003cp\u003e• The only English-language textbook describing the notions of convergence, boundedness, and summability with speed, as well as their applications in approximation theory\u003c\/p\u003e \u003cp\u003e• Compares the approximation orders of Fourier expansions in Banach spaces by different matrix methods\u003c\/p\u003e \u003cp\u003e• Matrix transforms of summability domains of regular perfect matrix methods are examined\u003c\/p\u003e \u003cp\u003e• Each chapter contains several solved examples and end-of-chapter exercises, including hints for solutions\u003c\/p\u003e \u003cp\u003e\u003ci\u003eAn Introductory Course in Summability Theory \u003c\/i\u003eis 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.\u003c\/p\u003e \u003cp\u003eANTS AASMA, PhD, is Associate Professor of Mathematical Economics in the Department of Economics and Finance at Tallinn University of Technology, Estonia.\u003c\/p\u003e \u003cp\u003eHEMEN DUTTA, PhD, is Senior Assistant Professor of Mathematics at Gauhati University, India.\u003c\/p\u003e \u003cp\u003eP.N. NATARAJAN, PhD, is Formerly Professor and Head of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India.\u003c\/p\u003e \u003cp\u003ePreface ix\u003cbr\u003e\u003cbr\u003eAbout the Authors xi\u003cbr\u003e\u003cbr\u003eAbout the Book xiii\u003cbr\u003e\u003cbr\u003e\u003cb\u003e1 Introduction and General Matrix Methods 1\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e1.1 Brief Introduction 1\u003cbr\u003e\u003cbr\u003e1.2 General Matrix Methods 2\u003cbr\u003e\u003cbr\u003e1.3 Exercise 16\u003cbr\u003e\u003cbr\u003eReferences 19\u003cbr\u003e\u003cbr\u003e\u003cb\u003e2 Special Summability Methods I 21\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e2.1 The Nörlund Method 21\u003cbr\u003e\u003cbr\u003e2.2 The Weighted Mean Method 29\u003cbr\u003e\u003cbr\u003e2.3 The Abel Method and the (C,1) Method 34\u003cbr\u003e\u003cbr\u003e2.4 Exercise 44\u003cbr\u003e\u003cbr\u003eReferences 45\u003cbr\u003e\u003cbr\u003e\u003cb\u003e3 Special Summability Methods II 47\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e3.1 The Natarajan Method and the Abel Method 47\u003cbr\u003e\u003cbr\u003e3.2 The Euler and Borel Methods 53\u003cbr\u003e\u003cbr\u003e3.3 The Taylor Method 59\u003cbr\u003e\u003cbr\u003e3.4 The Hölder and Cesàro Methods 62\u003cbr\u003e\u003cbr\u003e3.5 The Hausdorff Method 64\u003cbr\u003e\u003cbr\u003e3.6 Exercise 73\u003cbr\u003e\u003cbr\u003eReferences 74\u003cbr\u003e\u003cbr\u003e\u003cb\u003e4 Tauberian Theorems 75\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e4.1 Brief Introduction 75\u003cbr\u003e\u003cbr\u003e4.2 Tauberian Theorems 75\u003cbr\u003e\u003cbr\u003e4.3 Exercise 83\u003cbr\u003e\u003cbr\u003eReferences 84\u003cbr\u003e\u003cbr\u003e\u003cb\u003e5 Matrix Transformations of Summability and Absolute Summability Domains: Inverse-Transformation Method 85\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e5.1 Introduction 85\u003cbr\u003e\u003cbr\u003e5.2 Some Notions and Auxiliary Results 87\u003cbr\u003e\u003cbr\u003e5.3 The Existence Conditions of Matrix Transform Mx 91\u003cbr\u003e\u003cbr\u003e5.4 Matrix Transforms for Reversible Methods 95\u003cbr\u003e\u003cbr\u003e5.5 Matrix Transforms for Normal Methods 102\u003cbr\u003e\u003cbr\u003e5.6 Exercise 107\u003cbr\u003e\u003cbr\u003eReferences 109\u003cbr\u003e\u003cbr\u003e\u003cb\u003e6 Matrix Transformations of Summability and Absolute Summability Domains: Peyerimhoff’s Method 113\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e6.1 Introduction 113\u003cbr\u003e\u003cbr\u003e6.2 Perfect Matrix Methods 113\u003cbr\u003e\u003cbr\u003e6.3 The Existence Conditions of Matrix Transform Mx 117\u003cbr\u003e\u003cbr\u003e6.4 Matrix Transforms for Regular Perfect Methods 121\u003cbr\u003e\u003cbr\u003e6.5 Exercise 127\u003cbr\u003e\u003cbr\u003eReferences 129\u003cbr\u003e\u003cbr\u003e\u003cb\u003e7 Matrix Transformations of Summability and Absolute Summability Domains: The Case of Special Matrices 131\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e7.1 Introduction 131\u003cbr\u003e\u003cbr\u003e7.2 The Case of Riesz Methods 131\u003cbr\u003e\u003cbr\u003e7.3 The Case of Cesàro Methods 139\u003cbr\u003e\u003cbr\u003e7.4 Some Classes of Matrix Transforms 148\u003cbr\u003e\u003cbr\u003e7.5 Exercise 151\u003cbr\u003e\u003cbr\u003eReferences 154\u003cbr\u003e\u003cbr\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 On Convergence and Summability with Speed I\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction\u003c\/p\u003e \u003cp\u003e8.2 The sets (m\u003csup\u003eλ\u003c\/sup\u003e, m\u003csup\u003eμ\u003c\/sup\u003e), (c\u003csup\u003eλ\u003c\/sup\u003e, c\u003csup\u003eμ\u003c\/sup\u003e) and (c\u003csup\u003eλ\u003c\/sup\u003e, m\u003csup\u003eμ\u003c\/sup\u003e)\u003c\/p\u003e \u003cp\u003e8.3 Matrix transforms from m\u003csub\u003eA\u003c\/sub\u003e\u003csup\u003eλ\u003c\/sup\u003e into m\u003csub\u003eB\u003c\/sub\u003e\u003csup\u003eμ\u003c\/sup\u003e\u003c\/p\u003e \u003cp\u003e8.4 On orders of approximation of Fourier expansions\u003c\/p\u003e \u003cp\u003e8.5 Exercises\u003c\/p\u003e \u003cp\u003eReferences\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 On Convergence and Summability with Speed II\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction\u003c\/p\u003e \u003cp\u003e9.2 Some topological properties of m\u003csup\u003eλ\u003c\/sup\u003e, c\u003csup\u003eλ\u003c\/sup\u003e, c\u003csub\u003eA\u003c\/sub\u003e\u003csup\u003eλ\u003c\/sup\u003e and m\u003csub\u003eA\u003c\/sub\u003e\u003csup\u003eλ\u003c\/sup\u003e\u003c\/p\u003e \u003cp\u003e9.3 Matrix transforms from c\u003csub\u003eA\u003c\/sub\u003e\u003csup\u003eλ\u003c\/sup\u003e into c\u003csub\u003eB\u003c\/sub\u003e\u003csup\u003eμ\u003c\/sup\u003e or m\u003csub\u003eB\u003c\/sub\u003e\u003csup\u003eμ\u003c\/sup\u003e\u003c\/p\u003e \u003cp\u003e9.4 Exercises\u003c\/p\u003e \u003cp\u003eReferences\u003c\/p\u003e \\An Introductory Course in Summability Theory is the ideal rst 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.\" \u003cb\u003eMathematical Reviews, Sept 2017\u003c\/b\u003e   \u003cp\u003e\u003cb\u003e Ants Aasma, PhD,\u003c\/b\u003e is Associate Professor of Mathematical Economics in the Department of Economics and Finance at Tallinn University of Technology, Estonia.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003e Hemen Dutta, PhD,\u003c\/b\u003e is Senior Assistant Professor of Mathematics at Gauhati University, India.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003e P.N. Natarajan, PhD,\u003c\/b\u003e is Formerly Professor and Head of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India.       \u003c\/p\u003e\u003cp\u003e\u003cb\u003e An introductory course in summability theory for students, researchers, physicists, and engineers \u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 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.   \u003c\/p\u003e\u003cul\u003e \u003cli\u003eDiscusses results on matrix transforms of several matrix methods\u003c\/li\u003e \u003cli\u003eThe only English-language textbook describing the notions of convergence, boundedness, and summability with speed, as well as their applications in approximation theory\u003c\/li\u003e \u003cli\u003eCompares the approximation orders of Fourier expansions in Banach spaces by different matrix methods\u003c\/li\u003e \u003cli\u003eMatrix transforms of summability domains of regular perfect matrix methods are examined\u003c\/li\u003e \u003cli\u003eEach chapter contains several solved examples and end-of-chapter exercises, including hints for solutions\u003c\/li\u003e \u003c\/ul\u003e \u003cbr\u003e  \u003cp\u003e\u003ci\u003e An Introductory Course in Summability Theory\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988731543781,"sku":"NP9781119397694","price":145.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119397694.jpg?v=1761781368","url":"https:\/\/k12savings.com\/products\/an-introductory-course-in-summability-theory-isbn-9781119397694","provider":"K12savings","version":"1.0","type":"link"}