Classics in Mathematics

The Analysis of Linear Partial Differential Operators II

Differential Operators with Constant Coefficients

Authors: Hörmander, Lars

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-26964-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-540-22516-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.


About the authors

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. His book 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.

Reviews

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. Gouvêa, MathDL, January, 2005)


Table of contents (8 chapters)

  • Introduction

    Hörmander, Lars

    Pages 1-2

  • Existence and Approximation of Solutions of Differential Equations

    Hörmander, Lars

    Pages 3-59

  • Interior Regularity of Solutions of Differential Equations

    Hörmander, Lars

    Pages 60-93

  • The Cauchy and Mixed Problems

    Hörmander, Lars

    Pages 94-181

  • Differential Operators of Constant Strength

    Hörmander, Lars

    Pages 182-224

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-26964-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-540-22516-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
The Analysis of Linear Partial Differential Operators II
Book Subtitle
Differential Operators with Constant Coefficients
Authors
Series Title
Classics in Mathematics
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-26964-9
DOI
10.1007/b138375
Softcover ISBN
978-3-540-22516-4
Series ISSN
1431-0821
Edition Number
1
Number of Pages
XI, 395
Additional Information
Reprint of the 1983 Edition (Grundlehren der mathematischen Wissenschaften Vol. 257)
Topics