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This volume is an expanded version of Chapters III, IV, V and VII of my 1963 book "Linear partial differential operators". In addition there is an entirely new chapter on convolution equations, one on scattering theory, and one on methods from the theory of analytic functions of several complex variables. The latter is somewhat limited in scope though since it seems superfluous to duplicate the monographs by Ehrenpreis and by Palamodov on this subject. The reader is assumed to be familiar with distribution theory as presented in Volume I. Most topics discussed here have in fact been encountered in Volume I in special cases, which should provide the necessary motivation and background for a more systematic and precise exposition. The main technical tool in this volume is the Fourier- Laplace transformation. More powerful methods for the study of operators with variable coefficients will be developed in Volume III. However, constant coefficient theory has given the guidance for all that work. Although the field is no longer very active - perhaps because of its advanced state of development - and although it is possible to pass directly from Volume I to Volume III, the material presented here should not be neglected by the serious student who wants to gain a balanced perspective of the theory of linear partial differen­tial equations.

Operator theory --- Partial differential equations --- Differential equations, Partial --- Partial differential operators --- Equations aux dérivées partielles --- Opérateurs différentiels partiels --- 517.9 --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Equations aux dérivées partielles --- Opérateurs différentiels partiels --- Differential equations, Partial. --- Partial differential operators. --- Differentiaalvergelijkingen (Partiële). --- Differential equations, partial. --- Operator theory. --- Fourier analysis. --- Numerical analysis. --- Partial Differential Equations. --- Operator Theory. --- Fourier Analysis. --- Several Complex Variables and Analytic Spaces. --- Numerical Analysis. --- Mathematical analysis --- Analysis, Fourier --- Functional analysis --- Équations aux dérivées partielles --- Differential operators --- Partial differential equations. --- Functions of complex variables. --- Complex variables --- Elliptic functions --- Functions of real variables --- Topological groups. --- Lie groups. --- Topological Groups, Lie Groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Analyse fonctionnelle --- Fourier, Analyse de --- Functional analysis. --- Équations aux dérivées partielles --- Distributions, Théorie des (analyse fonctionnelle) --- Équations aux dérivées partielles.