P. N. Natarajan - Böcker

Sequence spaces and summability over valued fields is a research book aimed at research scholars, graduate students and teachers with an interest in Summability Theory both Classical (Archimedean) and Ultrametric (non-Archimedean).The book presents theory and methods in the chosen topic, spread over 8 chapters that seem to be important at research level in a still developing topic.Key FeaturesPresented in a self-contained mannerProvides examples and counterexamples in the relevant contextsProvides extensive references at the end of each chapter to enable the reader to do further research in the topicPresented in the same book, a comparative study of Archimedean and non-Archimedean Summability TheoryAppeals to young researchers and experienced mathematicians who wish to explore new areas in Summability TheoryThe book is written by a very experienced educator and researcher in Mathematical Analysis particularly Summability Theory.

An introductory course in summability theory for students, researchers, physicists, and engineersIn 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 solutionsAn 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.