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Asymptotics and borel summability

Author: O Costin
Publisher: Boca Raton : Chapman & Hall/CRC Press, ©2009.
Series: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 141.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
Providing a complete treatment of asymptotics, including exponential asymptotics and generalized Borel summability, this work provides a rigorous theoretical basis while also exploring applications to various problems in ordinary and partial differential equations and difference equations.
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: O Costin
ISBN: 9781420070316 1420070312
OCLC Number: 166379232
Description: xiii, 250 pages : illustrations ; 25 cm.
Contents: Introduction Expansions and approximationsFormal and actual solutionsReview of Some Basic Tools The Phragmen-Lindeloef theorem Laplace and inverse Laplace transformsClassical AsymptoticsAsymptotics of integrals: first resultsLaplace, stationary phase, saddle point methods, and Watson's lemma The Laplace method Watson's lemmaOscillatory integrals and the stationary phase methodSteepest descent method application: asymptotics of Taylor coefficients of analytic functionsBanach spaces and the contractive mapping principleExamplesSingular perturbationsWKB on a PDEAnalyzable Functions and Transseries Analytic function theory as a toy model of the theory of analyzable functions Transseries Solving equations in terms of Laplace transforms Borel transform, Borel summationGevrey classes, least term truncation, and Borel summationBorel summation as analytic continuation Notes on Borel summationBorel transform of the solutions of an example ODEAppendix: rigorous construction of transseriesBorel Summability in Differential Equations Convolutions revisited Focusing spaces and algebras Example: Borel summation of the formal solutions to (4.54) General setting Normalization procedures: an example Further assumptions and normalization Overview of results Further notation Analytic properties of Yk and resurgence Outline of the proofsAppendixAppendix: the C*-algebra of staircase distributions, D'm,vAsymptotic and Transasymptotic Matching; Formation of SingularitiesTransseries reexpansion and singularities: Abel's equation Determining the ξ reexpansion in practice Conditions for formation of singularities Abel's equation, continuedGeneral caseFurther examplesOther Classes of Problems Difference equationsPDEsOther Important Tools and Developments Resurgence, bridge equations, alien calculus, moulds Multisummability Hyperasymptotics References Index
Series Title: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 141.
Responsibility: Ovidiu Costin.
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Presents a treatment of asymptotics, including exponential asymptotics and generalized Borel summability. This work explores applications to various problems in ordinary and partial differential  Read more...

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"...Until the welcome publication of Ovidiu Costin's textbook on the subject, this more modern approach to asymptotic analysis was only accessible via original research papers and a few technical Read more...

 
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