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Introductory Course in Summability Theory (Hardcover) (Ants Aasma & P. N. Natarajan & Hemen Dutta)
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This book is designed as a text book for graduate students and researchers as a first course in summability theory. The book contains 9 chapters. In Chapter 1, after a very brief introduction to Summability Theory, general matrix methods are introduced and Silverman-Toeplitz theorem on regular matrices is discissed. Chapter 2 is devoted to a study of some special summability methods. The Norrland method, the Weighted Mean method, the Abel method, and the (C, 1) method are examined and their properties are discussed. Some more special summability methods are covered in Chapter 3, while Chapter 4 is devoted to a discussion of various Tauberian theorums involving certain summability methods. In Chapter 5, matrix transforms of summability and absolute summability domains of reversible and normal methods are examined. The notion of a perfect matrix method is introduced in Chapter 6, while Chapter 7 discusses matrix transforms of summability and absolute summability domains of the Cesaro and the Riesz methods. Next, in Chapter 8, the notions of the convergence and the boundedness of sequences with speed are introduced. Finally, Chapter 9 continues the investigation of convergence, boundedness and summability with speed, started in Chapter 8. Each chapter of the book contains several solved examples and chapter-end exercises including hints for solution.