The Analysis Of Linear Partial Differential Operators 2

Vol. II of Lars Hormander's 4-volume treatise is mainly devoted to operators with constant coefficients. From the reviews: "...these volumes are excellently written and make for greatly profitable reading. For years to come they will surely be a main reference for anyone wishing to study partial differential operators." Mathematical Reviews Vol. I of Lars Hormander's 4-volume treatise was an exposition of the theory of distributions and Fourier analysis preparing for the study of linear partial differential operators. 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.