Overview

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.

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9783540225164

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From the reviews: <p>.,. 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 <p> This volume focuses on linear partial differential operators with constant coefficients a ] . Each chapter ends with notes on the literature, and there is a large bibliography. a ] The binding of this softcover reprint seems quite good a ] . Overall, it is great to have this book back at an affordable price. It really does deserve to be described as a classic. (Fernando Q. GouvAaa, MathDL, January, 2005)

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 This volume focuses on linear partial differential operators with constant coefficients ! . Each chapter ends with notes on the literature, and there is a large bibliography. ! The binding of this softcover reprint seems quite good ! . Overall, it is great to have this book back at an affordable price. It really does deserve to be described as a classic. (Fernando Q. Gouvea, MathDL, January, 2005)

Author Information

Biography of Lars Hormander Born on January 24, 1931, on the southern coast of Sweden, Lars Hormander 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 Garding. 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. Hormander'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. His book Linear Partial Differential Operators published 1963 by Springer in the Grundlehren series was the first major account of this theory. Hid 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.

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