Algebraic Analysis

Algebraic Analysis

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

1st Edition - March 28, 1989

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  • Editors: Masaki Kashiwara, Takahiro Kawai
  • eBook ISBN: 9781483268026

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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

Product details

  • No. of pages: 494
  • Language: English
  • Copyright: © Academic Press 1989
  • Published: March 28, 1989
  • Imprint: Academic Press
  • eBook ISBN: 9781483268026

About the Editors

Masaki Kashiwara

Takahiro Kawai

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