Absolute Summability of Fourier Series and Orthogonal Series, Y. Okuyama

Автор: Delabaere
Название: Divergent Series, Summability and Resurgence III
ISBN: 3319289993 ISBN-13(EAN): 9783319289991
Издательство: Springer
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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: Mitschi
Название: Divergent Series, Summability and Resurgence I
ISBN: 3319287354 ISBN-13(EAN): 9783319287355
Издательство: Springer
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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
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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: Constantin
Название: Fourier Analysis
ISBN: 110762035X ISBN-13(EAN): 9781107620353
Издательство: Cambridge Academ
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Описание: A two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.

Автор: Constantin
Название: Fourier Analysis
ISBN: 1107044103 ISBN-13(EAN): 9781107044104
Издательство: Cambridge Academ
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Описание: A two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.

Автор: Ole G. Jorsboe; Leif Mejlbro
Название: The Carleson-Hunt Theorem on Fourier Series
ISBN: 3540111980 ISBN-13(EAN): 9783540111986
Издательство: Springer
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Автор: R. W. Bruggeman
Название: Fourier Coefficients of Automorphic Forms
ISBN: 3540108394 ISBN-13(EAN): 9783540108399
Издательство: Springer
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