An Introduction to Sato's HyperfunctionsThis book is a translation, with corrections and an updated bibliography, of Morimoto's 1976 book on the theory of hyperfunctions originally written in Japanese. Since the time that Sato established the theory of hyperfunctions, there have been many important applications to such areas as pseudodifferential operators and S-matrices. Assuming as little background as possible on the part of the reader, Morimoto covers the basic notions of the theory, from hyperfunctions of one variable to Sato's fundamental theorem. This book provides an excellent introduction to this important field of research. |
Contents
Analytic Functionals of One Variable | 23 |
Hyperfunctions of One Variable | 41 |
Cohomology Groups with Coefficients in a Sheaf | 69 |
Cohomology Groups with Coefficients in | 109 |
Analytic Functionals of Several Variables | 129 |
Hyperfunctions of Several Variables | 155 |
Microfunctions | 177 |
Development of Hyperfunction Theory | 211 |
Appendix A Linear Topological Spaces | 239 |
Appendix B Rudiments of Homological Algebra | 257 |
Bibliography | 265 |
Other editions - View all
An Introduction to Sato's Hyperfunctions Mitsuo Morimoto,Sato Chokansu Nyumon English No preview available - 1993 |
Common terms and phrases
Abelian groups Banach spaces canonical mapping Chapter closed set coefficients cohomology groups commutative compact set complex neighborhood converges convex set Corollary define definition denote diagram differential equations Edge-of-the-Wedge theorem Exp(E family of supports flabby resolution flabby sheaf following theorem Fourier-Borel transformation FS space holomorphic functions hyperfunction implies ind lim inductive limit injective isomorphism K₁ K₂ Lemma Let F linear mapping linear space linear topological space locally closed set locally convex space long exact sequence microfunctions open covering open neighborhood open set presheaf proof of Theorem properly convex PROPOSITION prove relative cohomology groups resp restriction mapping S. S. g S₁ S₂ satisfies the condition seminorms sequence of sheaves sheaf of germs special polyhedron Stein open set subset supp Suppose surjective system of seminorms T₁ T₂ theory of hyperfunctions topological space topology U₁ U₂ V₁ vanishes W₁ W₂
Popular passages
Page 1 - The main purpose of this chapter is to familiarize the reader with the notation, the definitions, and the theorems which will be used . frequently throughout this book.