Palamodov V.P. Linear Differential Operators with Constant Coefficients

Berlin: Springer, 1970. — 458 p.Preface
Table of Contents
Introduction
Exponential representation for an ordinary equation with one unknown function
Exponential representation of the solutions of partial differential equations
The exponential representation of solutions of arbitrary systems
Analytic Methods
Homological Tools
Families of topological modules
The fundamental homology theorem
Operations on modules
Division with Remainder in the Space of Power Series
The space of power series
The base sequence of matrices
Stabilization of the base sequence
p-decompositions
Cohomologies of Analytic Functions of Bounded Growth
The space of holomorphic functions
The operator Dz in spaces of type I
M-cohomologies
The theorem on the triviality of M-cohomologies
Cohomologies connected with P-matrices
The Fundamental Theorem
Some properties of finite P-modules
Local p-operators
The fundamental inequality for the operator D
Noetherian operators
The fundamental theorem
Differential Equations with Constant Coefficients
Linear Spaces and Distributions
Limiting processes in families of linear spaces
Functional spaces
Fourier transform
Homogeneous Systems of Equations
The exponential representation of solutions of homogeneous systems of equations
Hypoelliptic operators
Uniqueness of solutions of the Cauchy problem
Inhomogeneous Systems
Solubility of inhomogeneous systems. M-convexity
M-convexity in convex regions
The connection between M-convexity and the properties of a sheaf of solutions of a homogeneous system
The algebraic condition for M-convexity
Geometrical conditions of M-convexity
Operators of the form p(Dxi) in domains of holomorphy
Overdetermined Systems
Concerning the modules Ext^i(M, P)
The extension of solutions of homogeneous systems
The influence of boundary values on the behavior of the solutions within a region
Notes
Bibliography
Subject Index
Index of Basic Notation