Table Of ContentPROFESSOR MIKIO SATO
Algebraic Analysis
Papers Dedicated to Professor Mikio Sato on the
Occasion of His Sixtieth Birthday
Volume II
Edited by
Masaki Kashiwara
Takahiro Kawai
Research Institute for Mathematical Sciences
Kyoto University
Sakyo-ku, Kyoto
Japan
ACADEMIC PRESS, INC.
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Copyright © 1988 by Academic Press, Inc.
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United Kingdom Edition published by
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Library of Congress Cataloging-in-Publication Data
Algebraic analysis: papers dedicated to Professor Mikio Sato on the
occasion of his sixtieth birthday/edited by Masaki Kashiwara,
Takahiro Kawai.
p. cm.
Includes bibliographies and index.
ISBN 0-12-400465-2 (v. 1) ISBN 0-12-400466-0 (v. 2).
1. Mathematical analysis. 2. Algebra. 3. Sato, Mikio, Date-
I. Sato, Mikio, Date- II. Kashiwara, Masaki, Date-
Ill. Kawai, Takahiro.
QA300.A45 1988
515—dcl9 88-6331
CIP
Printed in the United States of America
89 90 91 92 9 8 7 6 5 4 3 2 1
Dedication
We and the contributors to this collection dedicate these articles on algebraic
analysis and related topics to Professor Mikio Sato.
We would like to celebrate the birthday of Professor Sato, initiator of
algebraic analysis in the twentieth century.
Congratulations on your sixtieth birthday, Professor Sato!
April 18, 1988
Editors
Michio Jimbo
Masaki Kashiwara
(co-editor-in-chief)
Takahiro Kawai
(co-editor-in-chief)
Hikosaburo Komatsu
Tetsuji Miwa
Mitsuo Morimoto
VOLUME EDITORS:
Michio Jimbo
Research Institute for Mathematical Sciences
Kyoto University
Sakyo-ku, Kyoto
Japan
Masaki Kashiwara
Research Institute for Mathematical Sciences
Kyoto University
Sakyo-ku, Kyoto
Japan
Takahiro Kawai
Research Institute for Mathematical Sciences
Kyoto University
Sakyo-ku, Kyoto
Japan
Hikosaburo Komatsu
Department of Mathematics
The University of Tokyo
Bunkyo-ku, Tokyo
Japan
Tetsuji Miwa
Research Institute for Mathematical Sciences
Kyoto University
Sakyo-ku, Kyoto
Japan
Mitsuo Morimoto
Department of Mathematics
Sophia University
Chiyoda-ku, Tokyo
Japan
Contents of Volume I
Introduction 1
Masaki Kashiwara and Takahiro Kawai
Three Personal Reminiscences 9
S. Iyanaga
Mikio Sato: Impressions 13
Gian-Carlo Rota
Sato, a Perfectionist 17
Kôsaku Yosida
Existence of Local Holomorphic Solutions of Differential Equations of Infinite
Order 19
Takashi Aoki
A Note on Holonomic q- Difference Systems 25
K. Aomoto
Solvable Models in Statistical Mechanics and Riemann Surfaces of Genus
Greater than One 29
Helen Au-Yang, Barry M. McCoy, Jacques H. H. Perk, and Shuang Tang
Linearization and Singular Partial Differential Equations 41
Gunter Bengel
On the Notions of Scattering State, Potential, and Wave-Function in Quantum
Field Theory: An Analytic-Functional Viewpoint 49
J. Bros
xi
xii Contents of Volume I
Two Remarks on Recent Developments in Solvable Models 75
Etsuro Date, Michio Jimbo, Tetsuji Miwa, and Masato Okado
Hypergeometric Functions 85
Leon Ehrenpreis
Quantization of Lie Groups and Lie Algebras 129
L. D. Faddeev, N. Yu. Reshetikhin, and L. A. Takhtajan
The Toda Lattice in the Complex Domain 141
H. Flaschka
Zoll Phenomena in (2 + 1) Dimensions 155
Victor Guillemin
A Proof of the Bott Inequalities 171
B. Helffer and J. Sjöstrand
What Is the Notion of a Complex Manifold with a Smooth Boundary? 185
C. Denson Hill
Toda Molecule Equations 203
Ryogo Hirota
Microlocal Analysis and Scattering in Quantum Field Theories 217
D. Iagolnitzer
b-Functions and p-adic Integrals 231
Jun-ichi Igusa
On the Poles of the Scattering Matrix for Several Convex Bodies 243
Mitsuru Ikawa
Symmetric Tensors of the A^l^ Family 253
Michio Jimbo, Tetsuji Miwa, and Masato Okado
On Hyperfunctions with Analytic Parameters 267
Akira Kaneko
The Invariant Holonomic System on a Semisimple Lie Group 277
Masaki Kashiwara
Contents of Volume I xiii
Some Applications of Microlocal Energy Methods to Analytic Hypoellipticity 287
Kiyômi Kataoka
A Proof of the Transformation Formula of the Theta-Functions 305
Yukiyosi Kawada
Microlocal Analysis of Infrared Singularities 309
Takahiro Kawai and Henry P. Stapp
On the Global Existence of Real Analytic Solutions of Systems of Linear
Differential Equations 331
Takahiro Kawai and Yoshitsugu Takei
Complex Powers on p-adic Fields and a Resolution of Singularities 345
Tatsuo Kimura
Operational Calculus, Hyperfunctions, and Ultradistributions 357
Hikosaburo Komatsu
On a Conjectural Equation of Certain Kinds of Surfaces 373
Michio Kuga
Vanishing Cycles and Second Microlocalization 381
Yves Laurent
Extensions of Microfunction Sheaves up to the Boundary 393
J.-L. Lieutenant
Extension of Holonomic 2-Modules 403
B. Malgrange
On the Irregularity of the Q) Holonomic Modules 413
x
Z. Mebkhout
An Error Analysis of Quadrature Formulas Obtained by Variable Transformation 423
Masatake Mori
Analytic Functionals on the Complex Light Cone and Their Fourier-Borel
Transformations 439
Mitsuo Morimoto and Ryoko Wada
A p-adic Theory of Hyperfunctions, II 457
Yasuo Morita
Contributors
Numbers in parentheses refer to the pages on which the authors' contributions begin. Numbers
smaller than 470 indicate contributions in Volume I.
Takashi Aoki (19), Department of Mathematics and Physics, Kinki University,
Kowakae 3-4-1, Higashi-Osaka-shi, Osaka 577, Japan
K. Aomoto (25), Department of Mathematics, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya 464, Japan
Helen Au-Yang (29), Institute for Theoretical Physics, State University of
New York at Stony Brook, Stony Brook, New York 11794-3840
Gunter Bengel (41), Mathematisches Institut der Westfälischen Wilhelms
Universität, Roxeler Strasse 64, 44 Münster, Federal Republic of Germany
J. Bros (49), Service de Physique Théorique, Institut de Recherche
Fondamentale, CFA, CEN-Saclay, B.P. 2, 91191 Gif-sur-Yvette Cédex,
France
Etsuro Date (75), Department of Mathematics, College of General Education,
Kyoto University, Yoshida-Nihonmatsu-cho, Sakyo-ku, Kyoto 606, Japan
Leon Ehrenpreis (85), Department of Mathematics, Temple University, Broad
St. and Montgomery Ave., Philadelphia, Pennsylvania 19122
L. D. Faddeev(129), SteklovInstitute, Fontanka27, Leningrad 191011, USSR
xv
xvi Contributors
H. Flaschka (141), Department of Mathematics, University of Arizona,
Tucson, Arizona 85721
Victor Guillemin (155), Department of Mathematics, Massachusetts Institute
of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
B. Helffer (171), Department of Mathematics, Université de Nantes, 44072
Nantes Cédex, France, and Centre de Mathématiques, Ecole Polytechnique,
91128 Palaiseau Cédex, France
C. Denson Hill (185), Department of Mathematics, State University of New
York at Stony Brook, Stony Brook, New York 11794-3840
Ryogo Hirota (203), Department of Applied Mathematics, Faculty of
Engineering, Hiroshima University, Oaza-Shitami, Saijo-cho, Higashi-
Hiroshima, Hiroshima 724, Japan
D. Iagolnitzer (217), Service de Physique Théorique, CEN-Saclay, Β.P. 2,
91190 Gif-sur-Yvette Cédex, France
Jun-ichi Igusa (231), Department of Mathematics, Johns Hopkins University,
Baltimore, Maryland 21218
Mitsuru Ikawa (243), Department of Mathematics, Osaka University,
Machikaneyama-cho 1-1, Toyonaka, Osaka 560, Japan
S. Iyanaga (9), Otsuka 6-12-4, Bunkyo-ku, Tokyo 112, Japan
Michio Jimbo (75, 253), Research Institute for Mathematical Sciences, Kyoto
University, Sakyo-ku, Kyoto 606, Japan
Akiro Kaneko (267), Department of Mathematics, University of Tokyo,
Komaba 3-8-1, Meguro-ku, Tokyo 153, Japan
Masaki Kashiwara (1, 277), Research Institute for Mathematical Sciences,
Kyoto University, Sakyo-ku, Kyoto 606, Japan
Kiyomi Kataoka (287), Department of Mathematics, Faculty of Science,
Tokyo Metropolitan University, Fukazawa, Setagaya-ku, Tokyo 158, Japan
Yukiyosi Kawada (305), Nagasaki 6-37-17, Toshima, Tokyo 171, Japan
