Description
Asymptotics and Borel Summability
Monographs and Surveys in Pure and Applied Mathematics Series
Author: Costin Ovidiu
Language: EnglishSubjects for Asymptotics and Borel Summability:
Keywords
Borel Summability; summation; Asymptotic Series; laplace; Laplace Transform; transform; Asymptotic Power Series; analytic; Watson’s Lemma; continuation; Asymptotic Expansion; inverse; Power Series; series; Banach Space; expansion; Formal Power Series; riemann; P F˜; surface; Riemann Lebesgue Lemma; Inverse Laplace Transform; Analytic Continuation; Exponentially Bounded; Equation Pi; Convergent Power Series; Follow; Singular Direction; Holds; Nonlinear ODEs; Finitely Generated; Banach Algebra; Borel Space; Convolution Equation; Nonresonance Condition
256 p. · 15.6x23.4 cm · Hardback
Description
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Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.
To give a sense of how new methods are used in a systematic way, the book analyzes in detail general nonlinear ordinary differential equations (ODEs) near a generic irregular singular point. It enables readers to master basic techniques, supplying a firm foundation for further study at more advanced levels. The book also examines difference equations, partial differential equations (PDEs), and other types of problems.
Chronicling the progress made in recent decades, this book shows how Borel summability can recover exact solutions from formal expansions, analyze singular behavior, and vastly improve accuracy in asymptotic approximations.
Introduction. Review of Some Basic Tools. Classical Asymptotics. Analyzable Functions and Transseries. Borel Summability in Differential Equations. Asymptotic and Transasymptotic Matching; Formation of Singularities. Other Classes of Problems. Other Important Tools and Developments. References. Index.