Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 1

466 Pages·1988·29.793 MB·English

by  Masaki Kashiwara, Takahiro Kawai

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PROFESSOR MIKIO SATO
Algebraic Analysis
Papers Dedicated to Professor Mikio Sato on the
Occasion of His Sixtieth Birthday
Volume I
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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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 II
KP Equations, Strings, and the Schottky Problem 473
Motohico Mulase
A Note on the Holonomic System of Invariant Hyperfunctions on a Certain
Prehomogeneous Vector Space 493
Masakazu Muro
Applications of Transformation Theory for Nonlinear Integrable Systems to Linear
Prediction Problems and Isospectral Deformations 505
Yoshimasa Nakamura
New Local Supersymmetry in the Framework of Einstein Gravity 517
Noburo Nakanishi
K2 Surfaces Related to Root Systems in EQ 527
Isao Naruki
Wronskian Determinants and the Gröbner Representation of a Linear Differential
Equation: An Approach to Nonlinear Integrable Systems 549
Masatoshi Noumi
Higher Codimensional Boundary Value Problem and F-Mild Hyperfunctions 571
Toshinori Oaku
Hodge Numbers of a Kummer Covering of P2 Ramified along a Line Configuration 587
Takayuki Oda
On a Stochastic Difference Equation for the Multi-Dimensional Weakly
Stationary Process with Discrete Time 601
Yasunori Okabe
XI
xii Contents of Volume II
Bäcklund Transformations of Classical Orthogonal Polynomials 647
Kazuo Okamoto
A Deformation of Dirichlet's Class Number Formula 659
Takashi Ono
A Method of Harmonic Analysis on Semisimple Symmetric Spaces 667
Toshio Oshima
A Note on Ehrenpreis' Fundamental Principle on a Symmetric Space 681
Toshio Oshima, Yutaka Saburi, and Masato Wakayama
Resurgence, Quantized Canonical Transformations, and Multi-lnstanton
Expansions 699
F. Pham
Quantization of Extended Vortices and sDiff R3 727
Mario Rasetti and Tullio Regge
Moduli Space for Fuchsian Groups 735
Kyoji Saito
The Hamburger Theorem for the Epstein Zeta Functions 789
Fumihiro Sato
Microfunctions for Boundary Value Problems 809
Pierre Schapira
Regularization of the Product of Complex Powers of Polynomials and Its
Application 821
Jiro Sekiguchi
On the Local Solvability of Fuchsian Type Partial Differential Equations 837
Hidetoshi Tahara
db-Cohomology and the Bochner-Martinelli Kernel 849
Shinichi Tajima
Issues of Multi-Dimensional Integrable Systems 853
K. Takasaki
Second Microlocalization and Conical Refraction (II) 867
Nobuyuki Tose
Contents of Volume II XIII
Pseudodifferential Operators in Hyperfunction Theory 883
Keisuke Uchikoshi
Some Observations on Geometrie Representations of the Superconformai
Algebras and a Super Analogue of the Mumford Sheaves 893
Kimio Ueno and Hirofumi Yamada
New Elliptic Solitons 901
J.-L. Verdier
On the Microlocal Smoothing Effect of Dispersive Partial Differential Equations, I:
Second-Order Linear Equations 911
Masao Yamazaki
Locally Prehomogeneous Spaces and Their Transverse Localizations 927
Tamaki Yano
On Carlson's Theorem for Holomorphic Functions 943
Kunio Yoshino
Contributors
Numbers in parentheses refer to the pages on which the authors' contributions begin. Numbers
greater than 470 indicate contributions in Volume II.
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, CFN-Saclay, B.P. 2, 91191 Gif-sur-Yvette Cedex,
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 Cedex, France, and Centre de Mathématiques, Ecole Polytechnique,
91128 Palaiseau Cedex, France
C. Derisori 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, B.P. 2,
91190 Gif-sur-Yvette Cedex, 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