Asymptotic analysis for integrable connections with irregular singular points. (English) Zbl 0546.58003

Majima, Hideyuki

Lecture Notes in Mathematics. 1075. Berlin etc.: Springer-Verlag. IX, 159 p DM 26.50; $ 9.30 (1984).

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.”

Reviewer: P.Michor

MSC:

58A17	Pfaffian systems
58-02	Research exposition (monographs, survey articles) pertaining to global analysis
35C20	Asymptotic expansions of solutions to PDEs
32L10	Sheaves and cohomology of sections of holomorphic vector bundles, general results

Keywords:

asymptotic expansions; Pfaffian systems; Riemann-Hilbert-Birkhoff problem; Poincaré’s lemma; de Rham cohomology