Hormander L. The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients

Springer-Verlag, 1983. — 392 p. — Series: Grundlehren Der Mathematischen Wissenschaften.
ISBN10: 0387121390 ISBN13: 978-0387121390.The present Vol. II is mainly devoted to operators with constant coefficients. An analysis of the existence and regularity of (fundamental) solutions in the first two chapters is followed by a thorough study of the Cauchy problem. One chapter is devoted to the spectral theory of short range perturbations of operators with constant coefficients, and another presents Fourier-Laplace representations of solutions of homogeneous differential equations with constant coefficients. The last chapter is a study of the closely related subject of convolution operators