Asymptotic analysis for integrable connections with irregular singular points / Hideyuki Majima

Auteur: Majima, Hideyuki (1952-) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1075Langue: anglaisÉditeur: Berlin : Springer-Verlag, 1984 ISBN: 9783540133759 Note: From the preface: ”Using strongly asymptotic expansions of functions of several (complex) variables, we prove existence theorems of asymptotic solutions to integrable systems of partial differential equations of the first order with irregular singular points under certain general conditions. We also prove analytic splitting lemmas for completely integrable linear Pfaffian systems. Moreover, for integrable connections with irregular singular points, we formulate and solve the Riemann- Hilbert-Birkhoff problem, and prove analogues of Poincaré’s lemma and de Rham cohomology theorem under certain general conditions.” Sujets MSC: 58A17 Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Pfaffian systems
58A15 Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Exterior differential systems (Cartan theory)
35C20 Partial differential equations -- Representations of solutions -- Asymptotic expansions
32L10 Several complex variables and analytic spaces -- Holomorphic fiber spaces -- Sheaves and cohomology of sections of holomorphic vector bundles, general results
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From the preface: ”Using strongly asymptotic expansions of functions of several (complex) variables, we prove existence theorems of asymptotic solutions to integrable systems of partial differential equations of the first order with irregular singular points under certain general conditions. We also prove analytic splitting lemmas for completely integrable linear Pfaffian systems. Moreover, for integrable connections with irregular singular points, we formulate and solve the Riemann- Hilbert-Birkhoff problem, and prove analogues of Poincaré’s lemma and de Rham cohomology theorem under certain general conditions.”

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