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Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations (Universitext)by Werner Balser
Synopses & Reviews
Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.
Includes bibliographical references (p. -288) and index.
Table of Contents
Basic Properties of Solutions.- Singularities of First Kind.- Highest Level Simplifications.- Asymptotic Power Series.- Integral Transforms.- Summable Power Series.- Cauchy-Heine Transform.- Solutions of Highest Level.- Acceleration Operators.- Multisummable Power Series.- Some Equivalent Definitions of Multisummability.- Matrices and Vector Spaces.- Functions with Values in Banach Spaces.- Functions of a Matrix.
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