The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis (Classics in Mathematics) by Lars Hörmander (PDF)

Description

The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen­ tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen­ eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.

User’s Reviews

Editorial Reviews: About the Author Biography of Lars HörmanderBorn 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. 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐First of all it must be said that I have only read and perused through these four volumes, and I purchased these books ca the year 2000. Albeit the first volume is suitable for a graduate or possibly advanced undergraduate course, the three remaining are comprehensive(basically he mentiones most things in the modern theory of linear PDE’s). Thus volume II, III and IV are technical and deep. Things like index theory and pseudo-differential operator theory are mentioned, but also Hamiltonian systems, first integrals, symplectic formulations, Fourier theory, variational principles, local analysis, certain problems related to quantum mechanics like Moller wave operator issues, etc.For specialists this is a must-read. But keep in mind that it requires time and effort to assimilate the remaining volumes(II, III, IV). Volume I is readily accessible, but specialists will not be primarily interested in I only, but also II, III and IV.I should point out that these four volumes are the foremost within the area. No other books go that far. You get what you bartered for if you invest the effort needed.Also, this is a classical reference. You may not know everything in these volumes, but you can refer to them and look up various issues in them. As such they are impeccable. Actually they are the classical reference.

⭐This is a classic textbook of Hormander. But please beware that this product is a reprint – it appears more like a photocopy of the original book. Most of the text is perfectly readable but the the printing is not sharp enough (as compared to the original print I’ve seen from my library). Some parts are even blurred (esp. small characters in the exponents, subscripts, etc.). I would rather recommend purchase directly from Springer.

⭐偏微分方程式の有名な本で、多くの本で推薦されている。基本事項が詳しく書かれている。

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