Автор: Hans-Heinrich K?¶rle Название: Infinite Series in a History of Analysis: Stages up to the Verge of Summability ISBN: 311034372X ISBN-13(EAN): 9783110343724 Издательство: Walter de Gruyter Цена: 37130.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: "Higher mathematics" once pointed towards the involvement of infinity. This we label analysis. The ancient Greeks had helped it to a first high point when they mastered the infinite. The book traces the history of analysis along the risky route of serial procedures through antiquity. It took quite long for this type of mathematics to revive in our region. When and where it did, infinite series proved the driving force. Not until a good two millennia had gone by, would analysis head towards Greek rigor again. To follow all that trial, error and final accomplishment, is more than studying history: It provides touching, worthwhile access to advanced calculus. Moreover, some steps beyond convergence show infinite series to naturally fit a wider frame.
Автор: Mitschi Название: Divergent Series, Summability and Resurgence I ISBN: 3319287354 ISBN-13(EAN): 9783319287355 Издательство: Springer Рейтинг: Цена: 41920.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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.
Автор: Loday-Richaud Название: Divergent Series, Summability and Resurgence II ISBN: 3319290746 ISBN-13(EAN): 9783319290744 Издательство: Springer Рейтинг: Цена: 41920.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations.The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided, which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya’s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations.This volume is the second in a series of three, entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes, it can be read independently.
Автор: P. N. Natarajan Название: Sequence Spaces and Summability Over Valued Fields ISBN: 0367236621 ISBN-13(EAN): 9780367236625 Издательство: Taylor&Francis Рейтинг: Цена: 117390.00 T Наличие на складе: Невозможна поставка. Описание: The main object of the present book is two-fold. Firstly, it supplements the comparatively small bulk of literature relating to sequence spaces and matrix transformations in non-archimedean analysis. Secondly, it illustrates how new proofs are necessary for proving the exact analogues of classical results.
Автор: Weisz Ferenc Название: Convergence and Summability of Fourier Transforms and Hardy Spaces ISBN: 3319860089 ISBN-13(EAN): 9783319860084 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces.
Автор: Ferenc Weisz Название: Convergence and Summability of Fourier Transforms and Hardy Spaces ISBN: 3319568132 ISBN-13(EAN): 9783319568133 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces.
Автор: Delabaere Название: Divergent Series, Summability and Resurgence III ISBN: 3319289993 ISBN-13(EAN): 9783319289991 Издательство: Springer Рейтинг: Цена: 41920.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The aim of this volume is two-fold. First, to show howthe resurgent methods introduced in volume 1 can be applied efficiently in anon-linear setting; to this end further properties of the resurgence theorymust be developed. Second, to analyze the fundamental example of the FirstPainlev? equation. The resurgent analysis of singularities is pushed all theway up to the so-called “bridge equation”, which concentrates allinformation about the non-linear Stokes phenomenon at infinity of the First Painlev?equation. The third in a series of three, entitled Divergent Series, Summability andResurgence, this volume is aimed at graduate students, mathematicians andtheoretical physicists who are interested in divergent power series and relatedproblems, such as the Stokes phenomenon. The prerequisites are a workingknowledge of complex analysis at the first-year graduate level and of thetheory of resurgence, as presented in volume 1.
Автор: Walter Ford Название: Studies on Divergent Series and Summability ISBN: 0472751417 ISBN-13(EAN): 9780472751419 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 27720.00 T Наличие на складе: Невозможна поставка. Описание: This publication is based on lectures and courses given by Walter Burton Ford at the University of Michigan about infinite series and divergent series. According to Ford, the study of divergent series can be divided into two parts, the first regarding asymptotic series and the second regarding the theory of summability, both of which are discussed within this volume.
Автор: Alabdulmohsin Название: Summability Calculus ISBN: 3319746472 ISBN-13(EAN): 9783319746470 Издательство: Springer Рейтинг: Цена: 79190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This book develops the foundations of 'summability calculus', which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.
