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An introductory course in summability theory for students, researchers, physicists, and engineers 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. • 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 solutions An 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.
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
This volume contains contributions from leading experts in the rapidly developing field of semigroup theory. The subject, now some 60 years old, began by imitating group theory and ring theory, but quickly developed an impetus of its own, and the semigroup turned out to be the most useful algebraic object in theoretical computer science.
Molecular Spectroscopy–XI provides information pertinent to the fundamental aspects of molecular spectroscopy. This book discusses the modifications of molecular spectra when the density varies as a function of temperature and pressure. Organized into 15 chapters, this book begins with an overview of the several processes concerning triplet excitons leading to magnetic-field sensitive luminescence in organic crystals and related compounds. This text then examines the methods of investigation of the exciton band structures in molecular crystals. Other chapters consider the conditions for the equivalence of Fourier spectroscopy and of slow passage experiments in nuclear magnetic resonance. This book discusses as well the application of computer technology in carbon-13 magnetic resonance spectroscopy. The final chapter deals with the application of high-resolution proton and carbon-13 n.m.r. spectroscopy for the investigation of the molecular conformations in proteins. This book is a valuable resource for organic chemists, biologists, microbiologists, scientists, and research workers.
Contents:Endomorphism Properties of Algebraic Structures (M E Adams et al.)Alternate Methods for Generating Interaction Semigroups (G R Barnes et al.)Separate vs. Joint Continuity: A Tale of Four Topologies — A Summary (M Henriksen)Cardinal Functions on Continuous Images (I Juhász)A Survey of Topological Nearrings and Nearrings of Continuous Functions (K D Magill, Jr.)Ordered Quotients and the Semi-Lattice of Ordered Compactifications (D D Mooney & T A Richmond)Various Topologies on Trees (P J Nyikos)Backward Shifts on Banach Spaces C(X), II (M Rajagopalan & K Sundaresan)and other papers Readership: Mathematicians.
This work is the first comprehensive assessment of Russia's foreign trade flows and economic growth in the seventeenth century. By demonstrating the growing openness of the economy, it reveals a key element in Russia's rise to great power status.
This book reports about the results of a Special Symposium “The Baltic Sea Basin”, held on August 11, 2008, within the frame of the 33rd IGC at Oslo, Norway in order to foster the understanding of the Baltic Basin as a unit in terms of genesis, structure, ongoing processes and utilization. It is the first time that in a joint publication, scientists from different disciplines give a comprehensive overview about the Baltic Sea basin in such a general sense. The book will be used not only by students and scientist but also by engineers and decision makers from industry and politics. Summarizing the state of the art in the investigation of the Baltic Sea Basin, but also in the resource utilisation of the basin the book will enhance the development of new monitoring strategies and technical device design including satellite observation methods, the establishment of international research laboratories, innovative topics for interdisciplinary research projects, etc.
The Annual Bibliography of the History of the Printed Book and Libraries records articles of scholarly value that relate to the history of the printed book, to the history of arts, crafts, techniques and equipment, and of the economic, social and cultural environment involved in their production, distribution, conservation and description.