Classical And Modern Methods In Summability

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Classical And Modern Methods In Summability

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Author : Johann Boos
language : en
Publisher: Clarendon Press
Release Date : 2000

Classical And Modern Methods In Summability written by Johann Boos and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

Summability is a mathematical topic with a long tradition and many applications in, for example, function theory, number theory, and stochastics. It was originally based on classical analytical methods, but was strongly influenced by modern functional analytical methods during the last seven decades. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Part I contains a short general introduction to summability, the basic classical theory concerning mainly inclusion theorems and theorems of the Silverman-Toeplitz type, a presentation of the most important classes of summability methods, Tauberian theorems, and applications of matrix methods. The proofs in Part I are exclusively done by applying classical analytical methods. Part II is concerned with modern functional analytical methods in summability, and contains the essential functional analytical basis required in later parts of the book, topologization of sequence spaces as K- and KF-spaces, domains of matrix methods as FK-spaces and their topological structure. In this part the proofs are of functional analytical nature only. Part III of the present book deals with topics in summability and topological sequence spaces which require the combination of classical and modern methods. It covers investigations of the constistency of matrix methods and of the bounded domain of matrix methods via Saks space theory, and the presentation of some aspects in topological sequence spaces. Lecturers, graduate students, and researchers working in summability and related topics will find this book a useful introduction and reference work.

An Introductory Course In Summability Theory

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Author : Ants Aasma
language : en
Publisher: John Wiley & Sons
Release Date : 2017-04-24

An Introductory Course In Summability Theory written by Ants Aasma and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-24 with Mathematics categories.

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 Universality Of The Radon Transform

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Author : Leon Ehrenpreis
language : en
Publisher: Oxford University Press, USA
Release Date : 2003

The Universality Of The Radon Transform written by Leon Ehrenpreis and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Written by a leading scholar in mathematics, this monograph discusses the Radon transform, a field that has wide ranging applications to X-ray technology, partial differential equations, nuclear magnetic resonance scanning and tomography. In this book, Ehrenpreis focuses on recent research and highlights the strong relationship between high-level pure mathematics and applications of the Radon transform to areas such as medical imaging.

2nd International Students Science Congress Proceedings

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Author : Mahamat Ali Amine Ouchar
language : en
Publisher: Infinite Study
Release Date :

2nd International Students Science Congress Proceedings written by Mahamat Ali Amine Ouchar and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

The aim of this study is to determine PstI polymorphism in the exon 6 region of the Pituitary-specific Transcription Factor (Pit-1) gene which is regarded as a candidate gene in mammals in regulating growth and development in 6 different goat breeds reared in Turkey. PstI polymorphism in Pit-1 gene (450 bp) was investigated by Restriction Fragment Length Polymorphism (RFLP) method in a total of 217 goats including 36 Hair, 18 Angora, 43 Kilis, 37 Honamlı, 46 Halep and 37 heads of Saanen breeds.

Some Novel Types Of Fractal Geometry

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Author : Stephen Semmes
language : en
Publisher: Oxford University Press
Release Date : 2001

Some Novel Types Of Fractal Geometry written by Stephen Semmes and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

The present book deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincaré inequalities, concerning the relationship between the average behaviour of a function and the average behaviour of its small-scale oscillations. Remarkable results in the last few years of Bourdon-Pajot and Laakso have shown that there is much more in the way of geometries like this than has been realized. Examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other hand, 'typical' fractals that might be seen in pictures do not have these same kinds of features. 'Some Novel Types of Fractal Geometry' will be of interest to graduate students and researchers in mathematics, working in various aspects of geometry and analysis.

Mathematical Analysis And Its Applications

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Author : Ferit Gürbüz
language : en
Publisher: CRC Press
Release Date : 2024-12-30

Mathematical Analysis And Its Applications written by Ferit Gürbüz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Mathematics categories.

This book covers contemporary topics in mathematical analysis and its applications and relevance in other areas of research. It provides a better understanding of methods, problems, and applications in mathematical analysis. It also covers applications and uses of operator theory, approximation theory, optimization, variable exponent analysis, inequalities, special functions, functional equations, statistical convergence and some function spaces, and presents various associated problems and ways to solve such problems. The book provides readers a better understanding of discussed research problems by presenting related developments in reasonable details. It strives to bring scientists, researchers and scholars together on a common platform.

Proceedings Of The Estonian Academy Of Sciences Physics And Mathematics

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Author :
language : en
Publisher:
Release Date : 2002-03

Proceedings Of The Estonian Academy Of Sciences Physics And Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03 with categories.

Advanced Functional Analysis

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Author : Eberhard Malkowsky
language : en
Publisher: CRC Press
Release Date : 2019-02-25

Advanced Functional Analysis written by Eberhard Malkowsky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-25 with Mathematics categories.

Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research.

Strange Functions In Real Analysis

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Author : Alexander Kharazishvili
language : en
Publisher: CRC Press
Release Date : 2017-10-16

Strange Functions In Real Analysis written by Alexander Kharazishvili and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-16 with Mathematics categories.

Strange Functions in Real Analysis, Third Edition differs from the previous editions in that it includes five new chapters as well as two appendices. More importantly, the entire text has been revised and contains more detailed explanations of the presented material. In doing so, the book explores a number of important examples and constructions of pathological functions. After introducing basic concepts, the author begins with Cantor and Peano-type functions, then moves effortlessly to functions whose constructions require what is essentially non-effective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, the author considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms. On the whole, the book is devoted to strange functions (and point sets) in real analysis and their applications.

Multi Dimensional Hyperbolic Partial Differential Equations

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Author : Sylvie Benzoni-Gavage
language : en
Publisher: OUP Oxford
Release Date : 2006-11-23

Multi Dimensional Hyperbolic Partial Differential Equations written by Sylvie Benzoni-Gavage and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-23 with Mathematics categories.

Authored by leading scholars, this comprehensive, self-contained text presents a view of the state of the art in multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. Ordered in sections of gradually increasing degrees of difficulty, the text first covers linear Cauchy problems and linear initial boundary value problems, before moving on to nonlinear problems, including shock waves. The book finishes with a discussion of the application of hyperbolic PDEs to gas dynamics, culminating with the shock wave analysis for real fluids. With an extensive bibliography including classical and recent papers both in PDE analysis and in applications (mainly to gas dynamics), this text will be valuable to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.