Divergent Series, Summability and Resurgence II: Simple and Multiple Summability
Springer | Analysis | Jun 29 2016 | ISBN-10: 3319290746 | 272 pages | pdf | 3.45 mb
Provides a thorough discussion and comparison of the theories of k-summability and multisummability
Can be treated both as a reference book and as a tutorial on the theories of summability and their links to the formal and local analytic aspects of linear ordinary differential equations
Includes a discussion of the linear Stokes phenomenon
The theories are illustrated with many examples and over 70 color figures
Addressing the question how to œsum 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 Sibuyas 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.
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