The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators (Classics in Mathematics) 2009th Edition by Lars Hörmander (PDF)

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From the reviews: “Volumes III and IV complete L. Hörmander’s treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades…..It is a superb book, which must be present in every mathematical library, and an indispensable tool for all – young and old – interested in the theory of partial differential operators.” L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987″This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (…) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation.” J. Brüning in Zentralblatt MATH, 1987Honours awarded to Lars Hörmander: Fields Medal 1962, Speaker at International Congress 1970, Wolf Prize 1988, AMS Steele Prize 2006

User’s Reviews

Editorial Reviews: Review From the reviews: “Volumes III and IV complete L. Hörmander’s treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades…..It is a superb book, which must be present in every mathematical library, and an indispensable tool for all – young and old – interested in the theory of partial differential operators.” L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987.”This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (…) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation.” J. Brüning in Zentralblatt MATH, 1987.“The fourth volume of the impressive monograph “The Analysis of Partial Differential Operators” by Lars Hörmander continues the detailed and unified approach of pseudo-differential and Fourier integral operators. The present book is a paperback edition of the fourth volume of this monograph. … The book has been one of the most elegant, inspiring and influential texts in Mathematics, and contains results used in many important developments in Partial Differential Equations and Mathematical Physics.” (Viorel Iftimie, Zentralblatt MATH, Vol. 1178, 2010) From the Back Cover From the reviews:”Volumes III and IV complete L. Hörmander’s treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades…..It is a superb book, which must be present in every mathematical library, and an indispensable tool for all – young and old – interested in the theory of partial differential operators.” L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987″This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (…) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation.” J. Brüning in Zentralblatt MATH, 1987 About the Author Biography 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. 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. Read more

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.

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