Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion of His Sixtieth BirthdayMasaki Kashiwara, Takahiro Kawai 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. |
Contents
| 1 | |
| 5 | |
| 9 | |
| 13 | |
| 17 | |
| 19 | |
| 25 | |
| 29 | |
Chapter 19 On the Poles of the Scattering Matrix for Several Convex Bodies | 243 |
Chapter 20 Symmetrie Tensors of the Α1n1 Family | 253 |
Chapter 21 On Hyperfunctions with Analytic Parameters | 267 |
Chapter 22 The Invariant Holonomic Systemon a Semisimple Lie Group | 277 |
Chapter 23 Some Applications of Microlocal Energy Methods to Analytic Hypoellipticity | 287 |
Chapter 24 A Proof of the Transformation Formula of the ThetaFunctions | 305 |
Chapter 25 Microlocal Analysis of Infrared Singularities | 309 |
Chapter 26 On the Global Existence of Real Analytic Solutions of Systems of Linear Differential Equations | 331 |
Chapter 7 Linearization and Singular Partial Differential Equations | 41 |
An AnalyticFunctional Viewpoint | 49 |
Chapter 9 Two Remarks on Recent Developments in Solvable Models | 75 |
Chapter 10 Hypergeometric Functions | 85 |
Chapter 11 Quantization of Lie Groups and Lie Algebras | 129 |
Chapter 12 The Toda Lattice in the Complex Domain | 141 |
Chapter 13 Zoll Phenomena in 2 + 1 Dimensions | 155 |
Chapter 14 A Proof of the Bott Inequalities | 171 |
Chapter 15 What is the Notion of a Complex Manifold with a Smooth Boundary? | 185 |
Chapter 16 Toda Molecule Equations | 203 |
Chapter 17 Microlocal Analysis and Scattering in Quantum Field Theories | 217 |
Chapter 18 bFunctions and padic Integrals | 231 |
Chapter 27 Complex Powers on padic Fields and a Resolution of Singularities | 345 |
Chapter 28Operational Calculus Hyperfunctions and Ultradistributions | 357 |
Chapter 29 On a Conjectural Equation of Certain Kinds of Surfaces | 373 |
Chapter 29 Vanishing Cycles and Second Microlocalization | 381 |
Chapter 30 Extensions of Microfunction Sheavesup to the Boundary | 393 |
Chapter 31 Extension of Holonomic Dmodules | 403 |
Chapter 32 On the Irregularity of the Dx Holonomic Modules | 413 |
Chapter 33 An Error Analysis of Quadrature Formulas Obtained by Variable Transformation | 423 |
Chapter 34 Analytic Functionals on the Complex Light Cone and Their FourierBorel Transformations | 439 |
Chapter 35 A padic Theory of Hyperfunctions II | 457 |
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1988 by Academic Academic Press admissible open Algebraic Analysis analytic functions asymptotic b-function boundary value Cartan coefficients cohomology compact complex manifold computation condition conformal group consider constant convex coordinates corresponding CR structure defined deformation denote Department of Mathematics differential equations differential operators eigenvalues exists Exp(S finite form reserved formula Fourier geometric Hence holomorphic function holonomic module hyperfunctions hypergeometric series integral invariant inverse irreducible Ising model isomorphism Japan Jimbo Kashiwara Kawai kernel Kyoto Kyoto University Laplace lattice Lemma Lie algebra light cone linear Math matrix microfunctions Microlocal Mikio Sato Miwa models molecule equation neighborhood obtained open subset parameters Phys polynomial proof properties Proposition prove real analytic relation representation resp rights of reproduction Sakyo-ku satisfies Sato scattering Section sheaf singularity solutions solvable space subspace surjective symbol Theorem Tokyo transformation Univ University vanishes vanishing cycles variables vector zero