Asymptotics of Linear Differential Equations

  • Authors
  • M. H. Lantsman

Part of the Mathematics and Its Applications book series (MAIA, volume 533)

Table of contents

  1. Front Matter
    Pages i-ix
  2. M. H. Lantsman
    Pages 1-13
  3. M. H. Lantsman
    Pages 14-37
  4. M. H. Lantsman
    Pages 38-48
  5. M. H. Lantsman
    Pages 49-89
  6. M. H. Lantsman
    Pages 144-182
  7. M. H. Lantsman
    Pages 183-205
  8. M. H. Lantsman
    Pages 354-377
  9. M. H. Lantsman
    Pages 420-424
  10. Back Matter
    Pages 425-441

About this book

Introduction

The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci­ ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp­ totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.

Keywords

Operator theory difference equation functional analysis functional equation ordinary differential equation

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9797-5
  • Copyright Information Springer Science+Business Media B.V. 2001
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5773-0
  • Online ISBN 978-94-015-9797-5
  • About this book
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