Lectures On Summability
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Lectures On Summability
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Author : Alexander Peyerimhoff
language : en
Publisher: Springer
Release Date : 2006-11-15
Lectures On Summability written by Alexander Peyerimhoff and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Classical Summability Theory
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Author : P.N. Natarajan
language : en
Publisher: Springer
Release Date : 2017-04-25
Classical Summability Theory written by P.N. Natarajan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-25 with Mathematics categories.
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 areas in Summability Theory..
Functional Analysis And Summability
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Author : P.N. Natarajan
language : en
Publisher: CRC Press
Release Date : 2020-09-07
Functional Analysis And Summability written by P.N. Natarajan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-07 with Mathematics categories.
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.
Divergent Series Summability And Resurgence I
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Author : Claude Mitschi
language : en
Publisher: Springer
Release Date : 2016-08-27
Divergent Series Summability And Resurgence I written by Claude Mitschi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-27 with Mathematics categories.
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.
An Introduction To Ultrametric Summability Theory
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Author : P.N. Natarajan
language : en
Publisher: Springer
Release Date : 2015-09-08
An Introduction To Ultrametric Summability Theory written by P.N. Natarajan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-08 with Mathematics categories.
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.
Coimbra Lecture Notes On Orthogonal Polynomials
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Author : Amilcar Jose Pinto Lopes Branquinho
language : en
Publisher: Nova Publishers
Release Date : 2008
Coimbra Lecture Notes On Orthogonal Polynomials written by Amilcar Jose Pinto Lopes Branquinho and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Orthogonal Polynomials and Special Functions (OPSF) have a very rich history, going back to 19th century when mathematicians and physicists tried to solve the most important deferential equations of mathematical physics. Hermite-Padé approximation was also introduced at that time, to prove the transcendence of the remarkable constant e (the basis of the natural logarithm). Since then OPSF has developed to a standard subject within mathematics, which is driven by applications. The applications are numerous, both within mathematics (e.g. statistics, combinatory, harmonic analysis, number theory) and other sciences, such as physics, biology, computer science, chemistry. The main reason for the fact that OPSF has been so successful over the centuries is its usefulness in other branches of mathematics and physics, as well as other sciences. There are many different aspects of OPSF. Some of the most important developments for OPSF are related to the theory of rational approximation of analytic functions, in particular the extension to simultaneous rational approximation to a system of functions. Important tools for rational approximation are Riemann-Hilbert problems, the theory of orthogonal polynomials, logarithmic potential theory, and operator theory for difference operators. This new book presents the latest research in the field.
Summability Theory And Its Applications
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Author : Feyzi Basar
language : en
Publisher: Bentham Science Publishers
Release Date : 2012-09-07
Summability Theory And Its Applications written by Feyzi Basar and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-07 with Mathematics categories.
The theory of summability has many uses throughout analysis and applied mathematics. Engineers and physicists working with Fourier series or analytic continuation will also find the concepts of summability theory valuable to their research. The concepts of summability have been extended to the sequences of fuzzy numbers and also to the theorems of ergodic theory. This ebook explains various aspects of summability and demonstrates applications in a coherent manner. The content can readily serve as a useful series of lecture notes on the subject. This ebook comprises of 8 chapters starting from classical sequence spaces and covering matrix transformations and fuzzy numbers. An accompanying bibliography with extensive references makes this a valuable source of information for readers interested in summability theory as well as other branches of science.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Symmetries And Related Topics In Differential And Difference Equations
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Author : David Blázquez-Sanz
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Symmetries And Related Topics In Differential And Difference Equations written by David Blázquez-Sanz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The papers collected here discuss topics such as Lie symmetries, equivalence transformations and differential invariants, group theoretical methods in linear equations, and the development of some geometrical methods in theoretical physics. The reader will find new results in symmetries of differential and difference equations, applications in classical and quantum mechanics, two fundamental problems of theoretical mechanics, and the mathematical nature of time in Lagrangian mechanics.
Lectures On Algebraic And Differential Topology
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Author : R. Bott
language : en
Publisher: Springer
Release Date : 2006-11-15
Lectures On Algebraic And Differential Topology written by R. Bott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.