Algebraic Analysis - 1st Edition - ISBN: 9780124004658, 9781483268026

Algebraic Analysis

1st Edition

Papers Dedicated to Professor Mikio Sato on the Occasion of His Sixtieth Birthday

Editors: Masaki Kashiwara Takahiro Kawai
eBook ISBN: 9781483268026
Imprint: Academic Press
Published Date: 28th March 1989
Page Count: 494
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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.

Table of Contents

Contents of Volume II



Three Personal Reminiscences

Mikio Sato: Impressions

Sato, A Perfectionist

Existence of Local Holomorphic Solutions of Differential Equations of Infinite Order

A Note on Holonomic q-Difference Systems

Solvable Models in Statistical Mechanics and Riemann Surfaces of Genus Greater than One

Linearization and Singular Partial Differential Equations

On the Notions of Scattering State, Potential, and Wave-Function in Quantum Field Theory: An Analytic-Functional Viewpoint

Two Remarks on Recent Developments in Solvable Models

Hypergeometric Functions

Quantization of Lie Groups and Lie Algebras

The Toda Lattice in the Complex Domain

Zoll Phenomena in (2 + 1) Dimensions

A Proof of the Bott Inequalities

What is the Notion of a Complex Manifold with a Smooth Boundary?

Toda Molecule Equations

Microlocal Analysis and Scattering in Quantum Field Theories

b-Functions and p-Adic Integrals

On the Poles of the Scattering Matrix for Several Convex Bodies

Symmetric Tensors of the A(1)n-1 Family

On Hyperfunctions with Analytic Parameters

The Invariant Holonomic System on a Semisimple Lie Group

Some Applications of Microlocal Energy Methods to Analytic Hypoellipticity

A Proof of the Transformation Formula of the Theta-Functions

Microlocal Analysis of Infrared Singularities

On the Global Existence of Real Analytic Solutions of Systems of Linear Differential Equations

Complex Powers on p-Adic Fields and a Resolution of Singularities

Operational Calculus, Hyperfunctions, and Ultradistributions

On a Conjectural Equation of Certain Kinds of Surfaces

Vanishing Cycles and Second Microlocalization

Extensions of Microfunction Sheaves Up to the Boundary

Extension of Holonomic 𝒟-Modules

On the Irregularity of the 𝒟x Holonomic Modules

An Error Analysis of Quadrature Formulas Obtained by Variable Transformation

Analytic Functionals on the Complex Light Cone and their Fourier-Borel Transformations

A p-Adic Theory of Hyperfunctions, II


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© Academic Press 1988
Academic Press
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About the Editor

Masaki Kashiwara

Takahiro Kawai

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