In this second volume (4 volume work), Lars Hörmander looks at 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. He then moves on to cover spectral theory of short range perturbations of operators with constant coefficients, and Fourier-Laplace representations of solutions of homogeneous differential equations with constant coefficients. The last chapter presents a study of the closely related subject of convolution operators.

Autorentext

Biography of Lars Hörmander

Born on January 24, 1931, on the southern coast of Sweden, Lars Hörmander did his secondary schooling as well as his undergraduate and doctoral studies in Lund. His principle teacher and adviser at the University of Lund was Marcel Riesz until he returned, then Lars Gårding. In 1956 he worked in the USA, at the universities of Chicago, Kansas, Minnesota and New York, before returning to a chair at the University of Stockholm. He remained a frequent visitor to the US, particularly to Stanford and was Professor at the IAS, Princeton from 1964 to 1968. In 1968 he accepted a chair at the University of Lund, Sweden, where, today, he is Emeritus Professor.

Hörmander's lifetime work has been devoted to the study of partial differential equations and its applications in complex analysis. In 1962 he was awarded the Fields Medal for his contributions to the general theory of linear partial differential operators. Hisbook Linear Partial Differential Operators published 1963 by Springer in the Grundlehren series was the first major account of this theory. His four volume text The Analysis of Linear Partial Differential Operators published in the same series 20 years later illustrates the vast expansion of the subject in that period.