An Introductory Course in Summability Theory. (2017)

• Record Type: Book
• Further Information: Note: Ants Aasma, Hemen Dutta, P. N. Natarajan.
• Authors: Aasma, Ants; Dutta, Hemen; Natarajan, P. N
• Contents: Preface ix; ; About the Authors xi; ; About the Book xiii; ; 1 Introduction and General Matrix Methods 1; ; 1.1 Brief Introduction 1; ; 1.2 General Matrix Methods 2; ; 1.3 Exercise 16; ; References 19; ; 2 Special Summability Methods I 21; ; 2.1 The Nörlund Method 21; ; 2.2 The Weighted Mean Method 29; ; 2.3 The Abel Method and the (C, 1) Method 34; ; 2.4 Exercise 44; ; References 45; ; 3 Special Summability Methods II 47; ; 3.1 The Natarajan Method and the Abel Method 47; ; 3.2 The Euler and Borel Methods 53; ; 3.3 The Taylor Method 59; ; 3.4 The Hölder and Cesàro Methods 62; ; 3.5 The Hausdorff Method 64; ; 3.6 Exercise 73; ; References 74; ; 4 Tauberian Theorems 75; ; 4.1 Brief Introduction 75; ; 4.2 Tauberian Theorems 75; ; 4.3 Exercise 83; ; References 84; ; 5 Matrix Transformations of Summability and Absolute Summability Domains: Inverse-Transformation Method 85; ; 5.1 Introduction 85; ; 5.2 Some Notions and Auxiliary Results 87; ; 5.3 The Existence Conditions of Matrix Transform Mx 91; ; 5.4 Matrix Transforms for Reversible Methods 95; ; 5.5 Matrix Transforms for Normal Methods 102; ; 5.6 Exercise 107; ; References 109; ; 6 Matrix Transformations of Summability and Absolute Summability Domains: Peyerimhoff’s Method 113; ; 6.1 Introduction 113; ; 6.2 Perfect Matrix Methods 113; ; 6.3 The Existence Conditions of Matrix Transform Mx 117; ; 6.4 Matrix Transforms for Regular Perfect Methods 121; ; 6.5 Exercise 127; ; References 129; ; 7 Matrix Transformations of Summability and Absolute Summability Domains: The Case of Special Matrices 131; ; 7.1 Introduction 131; ; 7.2 The Case of Riesz Methods 131; <br />7.3 The Case of Cesàro Methods 139; ; 7.4 Some Classes of Matrix Transforms 148; ; 7.5 Exercise 151; ; References 154; ; 8 On Convergence and Summability with Speed I 157; ; 8.1 Introduction 157; ; 8.2 The Sets (m, m), (c, c), and (c, m) 159; ; 8.3 Matrix Transforms from mA into mB 164; ; 8.4 On Orders of Approximation of Fourier Expansions 171; ; 8.5 Exercise 177; ; References 179; ; 9 On Convergence and Summability with Speed II 183; ; 9.1 Introduction 183; ; 9.2 Some Topological Properties of m, c, c A and mA 184; ; 9.3 Matrix Transforms from cA into cB or mB 188; ; 8.5 Exercise 196; ; References 197; ; Index 199
• Edition: 1st
• Publisher Details: Wiley
• Publication Date: 2017
• Extent: 1 online resource (224 pages)
• Subjects: 515.243
• Languages: English
• ISBNs: 9781119397779
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.