تحلیل جبری. مقالاتی تقدیم به پروفسور میکیو ساتو به مناسبت شصتمین سالگرد تولدش، جلد اول

Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion of his 60th Birthday, Volume I is a collection of research papers on algebraic analysis and related topics in honor to Professor Mikio Sato's 60th birthday. This volume is composed of 35 chapters and begins with papers concerning Sato's early career in algebraic analysis. The succeeding chapters deal with research works on the existence of local holomorphic solutions, the holonomic q-difference systems, partial differential equations, and the properties of solvable models. Other chapters explore the fundamentals of hypergeometric functions, the Toda lattice in the complex domain, the Lie algebras, b-functions, p-adic integrals, analytic parameters of hyperfunctions, and some applicatioins of microlocal energy methods to analytic hypoeellipticity. This volume also presents studies on the complex powers of p-adic fields, operational calculus, extensions of microfunction sheaves up to the boundary, and the irregularity of holonomic modules. The last chapters feature research works on error analysis of quadrature formulas obtained by variable transformation and the analytic functional on the complex light cone, as well as their Fourier-Borel transformations. This book will prove useful to mathematicians and advance mathematics students. Content: Inside Front Cover, Page ii Front Matter, Page iii Copyright, Page iv Dedication, Page v VOLUME EDITORS, Page vi Contents of Volume II, Pages xi-xiii Contributors, Pages xv-xxi Introduction, Pages 1-7 Three Personal Reminiscences, Pages 9-11, S. Iyanaga Mikio Sato: Impressions, Pages 13-15, Gian-Carlo Rota Sato, a Perfectionist, Pages 17-18, Kôsaku Yosida Existence of Local Holomorphic Solutions of Differential Equations of Infinite Order, Pages 19-24, Takashi Aoki A Note on Holonomic q- Difference Systems, Pages 25-28, K. Aomoto Solvable Models in Statistical Mechanics and Riemann Surfaces of Genus Greater than One, Pages 29-39, Helen Au-Yang, Barry M. McCoy, Jacques H.H. Perk, Shuang Tang Linearization and Singular Partial Differential Equations, Pages 41-47, Gunter Bengel On the Notions of Scattering State, Potential and Wave-Function in Quantum Field Theory: An Analytic-Functional Viewpoint, Pages 49-73, J. Bros Two Remarks on Recent Developments in Solvable Models, Pages 75-84, Etsuro Date, Michio Jimbo, Tetsuji Miwa, Masato Okado Hypergeometric Functions, Pages 85-128, Leon Ehrenpreis Quantization of Lie Groups and Lie Algebras, Pages 129-139, L.D. Faddeev, N.Yu. Reshetikhin, L.A. Takhtajan The Toda Lattice in the Complex Domain, Pages 141-154, H. Flaschka Zoll Phenomena in (2 + 1) Dimensions, Pages 155-169, Victor Guillemin A Proof of the Bott Inequalities, Pages 171-183, B. Helffer, J. Sjöstrand What is the Notion of a Complex Manifold with a Smooth Boundary?, Pages 185-201, C. Denson Hill Toda Molecule Equations, Pages 203-216, Ryogo Hirota Microlocal Analysis and Scattering in Quantum Field Theories, Pages 217-230, D. lagolnitzer b-Functions and p-adic Integrals, Pages 231-241, Jun-ichi Igusa On the Poles of the Scattering Matrix for Several Convex Bodies, Pages 243-251, Mitsuru Ikawa Symmetric Tensors of the Family, Pages 253-266, Michio Jimbo, Tetsuji Miwa, Masato Okado On Hyperfunctions with Analytic Parameters, Pages 267-276, Akira Kaneko The Invariant Holonomic System on a Semisimple Lie Group, Pages 277-286, Masaki Kashiwara Some Applications of Microlocal Energy Methods to Analytic Hypoellipticity, Pages 287-303, Kiyômi Kataoka A Proof of the Transformation Formula of the Theta-Functions, Pages 305-308, Yukiyosi Kawada Microlocal Analysis of Infrared Singularities, Pages 309-330, Takahiro Kawai, Henry P. Stapp On the Global Existence of Real Analytic Solutions of Systems of Linear Differential Equations, Pages 331-344, Takahiro Kawai, Yoshitsugu Takei Complex Powers on p-adic Fields and a Resolution of Singularities, Pages 345-355, Tatsuo Kimura Operational Calculus, Hyperfunctions and Ultradistributions, Pages 357-372, Hikosaburo Komatsu On a Conjectural Equation of Certain Kinds of Surfaces, Pages 373-379, Michio Kuga Vanishing Cycles and Second Microlocalization, Pages 381-391, Yves Laurent Extensions of Microfunction Sheaves up to the Boundary, Pages 393-401, J.-L. Lieutenant Extension of Holonomic -modules, Pages 403-411, B. Malgrange On the Irregularity of the Holonomic Modules, Pages 413-421, Z. Mebkhout An Error Analysis of Quadrature Formulas Obtained by Variable Transformation, Pages 423-437, Masatake Mori Analytic Functionals on the Complex Light Cone and Their Fourier-Borel Transformations, Pages 439-455, Mitsuo Morimoto, Ryoko Wada A p-adic Theory of Hyperfunctions, II, Pages 457-472, Yasuo Morita