an:03870247
Zbl 0546.58003
Majima, Hideyuki
Asymptotic analysis for integrable connections with irregular singular points
EN
Lecture Notes in Mathematics. 1075. Berlin etc.: Springer-Verlag. IX, 159 p DM 26.50; {\$} 9.30 (1984).
00379673
1984
b
58A17 58-02 35C20 32L10
asymptotic expansions; Pfaffian systems; Riemann-Hilbert-Birkhoff problem; Poincar??'s lemma; de Rham cohomology
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 Poincar??'s lemma and de Rham cohomology theorem under certain general conditions.''
P.Michor