Algebraic analysis of differential equations : From microlocal analysis to exponential asymptotics ; Festschrift in honor of Takahiro Kawai ; [articles in part II of this volume were read at the Conference "Algebraic Analysis of Differential Equations - f

This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference ''Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics'' at Kyoto University in 2005. Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas, providing interested researchers and students with valuable suggestions and instructive guidance for their work. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics. This dedication is made on the occasion of Professor Kawai's 60th birthday as a token of deep appreciation of the important contributions he has made to the field. Introductory notes on the scientific works of Professor Kawai are also included. 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations - from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. The articles contained here present many new results and ideas, providing interested researchers and students with valuable suggestions and instructive guidance for their work."--Jacket