Asymptotics And Borel Summability
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Asymptotics and Borel Summability
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, tr
Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation
Author: Ovidiu Costin
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-02-21
These are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, small denominator questions, new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, a new family of resurgent functions related to knot theory.
Asymptotic Expansions and Summability
This book provides a comprehensive exploration of the theory of summability of formal power series with analytic coefficients at the origin of Cn, aiming to apply it to formal solutions of partial differential equations (PDEs). It offers three characterizations of summability and discusses their applications to PDEs, which play a pivotal role in understanding physical, chemical, biological, and ecological phenomena. Determining exact solutions and analyzing properties such as dynamic and asymptotic behavior are major challenges in this field. The book compares various summability approaches and presents simple applications to PDEs, introducing theoretical tools such as Nagumo norms, Newton polygon, and combinatorial methods. Additionally, it presents moment PDEs, offering a broad class of functional equations including classical, fractional, and q-difference equations. With detailed examples and references, the book caters to readers familiar with the topics seeking proofs or deeper understanding, as well as newcomers looking for comprehensive tools to grasp the subject matter. Whether readers are seeking precise references or aiming to deepen their knowledge, this book provides the necessary tools to understand the complexities of summability theory and its applications to PDEs.