Algebraic Analysis
Papers Dedicated to Professor Mikio Sato on the Occasion of His Sixtieth Birthday
- 1st Edition - September 25, 2014
- Editors: Masaki Kashiwara, Takahiro Kawai
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 1 3 7 - 1
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 8 0 2 - 6
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… Read more
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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.
Contents of Volume II
Contributors
Introduction
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
- Edition: 1
- Published: September 25, 2014
- Language: English
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