Algebraic analysis of differential equations

This is a collection of articles on algebraic analysis of di?erential equations and related topics. The contributors (T. Kawaiexcepted) and we, the editors, dedicate this volume to ProfessorTakahiroKAWAI,who is one ofthe creators of microlocal analysis, a central object of the subjects. To respect his many substantial contributions to the subjects, we have included some explanatory notes about the work of Professor T. Kawai in Part I of the volume. Most of the contributed articles in Part II of this volume were read at the Conference “Algebraic Analysis of Di?erential Equations — from Micro- cal Analysis to Exponential Asymptotics”, which we organized from July 7 through July 14, 2005 at the Research Institute for Mathematical Sciences, Kyoto University to celebrate Professor T. Kawai’s sixtieth birthday. Taking this opportunity, we would like to express once again our sincerest congra- lations to Professor Kawai. Kyoto in Japan, Takashi Aoki June 27, 2007 Hideyuki Majima Yoshitsugu Takei Nobuyuki Tose Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX Part I The work of T. Kawai Publications of Professor Takahiro Kawai . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The work of T. Kawai on hyperfunction theory and microlocal analysis, Part 1 — Microlocal analysis and di?erential equations Nobuyuki Tose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The work of T. Kawai on hyperfunction theory and microlocal analysis, Part 2 — Operators of in?nite order and convolution equations Takashi Aoki. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 The work of T. Kawai on exact WKB analysis Yoshitsugu Takei. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .