There are excellent books on both functional analysis and summability. Most of them are very terse. In Functional Analysis and Summability, the author makes a sincere attempt for a gentle introduction of these topics to students. In the functional analysis component of the book, the Hahn–Banach theorem, Banach–Steinhaus theorem (or uniform boundedness principle), the open mapping theorem, the closed graph theorem, and the Riesz representation theorem are highlighted. In the summability component of the book, the Silverman–Toeplitz theorem, Schur’s theorem, the Steinhaus theorem, and the Steinhaus-type theorems are proved. The utility of functional analytic tools like the uniform boundedness principle to prove some results in summability theory is also pointed out.Features A gentle introduction of the topics to the students is attempted. Basic results of functional analysis and summability theory and their applications are highlighted. Many examples are provided in the text. Each chapter ends with useful exercises.This book will be useful to postgraduate students, pre-research level students, and research scholars in mathematics. Students of physics and engineering will also find this book useful since topics in the book also have applications in related areas.
Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents, for the first time, a brief survey of the research to date in ultrametric summability theory, which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis.
This is the second, completely revised and expanded edition of the author’s first book, covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents a brief survey of the research to date in ultrametric summability theory, which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis. The book is also useful as a text for those who wish to specialize in ultrametric summability theory.
This is the second, completely revised and expanded edition of the author’s first book, covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents a brief survey of the research to date in ultrametric summability theory, which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis. The book is also useful as a text for those who wish to specialize in ultrametric summability theory.
This book presents results about certain summability methods, such as the Abel method, the Norlund method, the Weighted mean method, the Euler method and the Natarajan method, which have not appeared in many standard books. It proves a few results on the Cauchy multiplication of certain summable series and some product theorems. It also proves a number of Steinhaus type theorems. In addition, it introduces a new definition of convergence of a double sequence and double series and proves the Silverman-Toeplitz theorem for four-dimensional infinite matrices, as well as Schur's and Steinhaus theorems for four-dimensional infinite matrices. The Norlund method, the Weighted mean method and the Natarajan method for double sequences are also discussed in the context of the new definition. Divided into six chapters, the book supplements the material already discussed in G.H.Hardy's Divergent Series. It appeals to young researchers and experienced mathematicians who wish to explore new areasin Summability Theory..
This book presents results about certain summability methods, such as the Abel method, the Norlund method, the Weighted mean method, the Euler method and the Natarajan method, which have not appeared in many standard books. It proves a few results on the Cauchy multiplication of certain summable series and some product theorems. It also proves a number of Steinhaus type theorems. In addition, it introduces a new definition of convergence of a double sequence and double series and proves the Silverman-Toeplitz theorem for four-dimensional infinite matrices, as well as Schur's and Steinhaus theorems for four-dimensional infinite matrices. The Norlund method, the Weighted mean method and the Natarajan method for double sequences are also discussed in the context of the new definition. Divided into six chapters, the book supplements the material already discussed in G.H.Hardy's Divergent Series. It appeals to young researchers and experienced mathematicians who wish to explore new areasin Summability Theory..
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 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.
In the commercial vapour absorption refrigeration system a heating coil generator system is usually employed to vaporize the ammonia refrigerant. In this book work, the theoretical investigations were presented by replacing the heating coil generator system with the frame plate type heat exchanger. By the way, the exhaust gases from the IC engine have been utilized to vaporize the ammonia refrigerant. The available heat in the exhaust gases was estimated based on actual IC Engine driving cycles. The frame plate type heat exchanger has been modeled and flow analysis inside the heat exchanger was conducted with the help of CFD packages. In addition, the recoverable energy of the exhaust gases was analyzed for the representative IC Engine.
What could go wrong when two recently retired oddball cops from Washington, D.C. dive head first in search of gold in Afghanistan and a buried fortune in Mexico? A lot After a moderate success in Afghanistan Sal Rossi and Danny Mahoney plot a search for a buried horde of gold coins of incalculable value that was buried during the 1914 Mexican revolution then lost to the winds of history. The good news is that the two adventurists eventually find the location of the crates, the bad news is the town is dominated by a ruthless drug lord named Cicatriz (The scar). While attempting to unearth the crates and on their way to riches, they're interrupted by cartel gang members who have different plans for them and the treasure.P.N.G. is a fictionalized account based on real events of two former cop's adrenaline rush search for riches that's interspersed with moments of comedy and friendship but with unmistakable undercurrents of extreme danger. Whether you're an armchair adventurer or someone who's been there done that, don't miss this action-packed story.
Title: Het Oudste leenactenboek van Gelre, 1326. Naar het oorspronkelijke handschrift uitgegeven door P. N. v. Doorninck.Publisher: British Library, Historical Print EditionsThe British Library is the national library of the United Kingdom. It is one of the world's largest research libraries holding over 150 million items in all known languages and formats: books, journals, newspapers, sound recordings, patents, maps, stamps, prints and much more. Its collections include around 14 million books, along with substantial additional collections of manuscripts and historical items dating back as far as 300 BC.The HISTORY OF EUROPE collection includes books from the British Library digitised by Microsoft. This collection includes works chronicling the development of Western civilisation to the modern age. Highlights include the development of language, political and educational systems, philosophy, science, and the arts. The selection documents periods of civil war, migration, shifts in power, Muslim expansion into Central Europe, complex feudal loyalties, the aristocracy of new nations, and European expansion into the New World. ++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification: ++++ British Library Anonymous; Doorninck, P N. van; 1898. 34 p.; 8 . 010271.f.16.
