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The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed, leading up to Trépreau’s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category. At the beginning of the book, no prerequisites are assumed beyond calculus and linear algebra. Later on, basic facts from distribution theory and functional analysis are needed. In a few places, a more extensive background in differential geometry or pseudodifferential calculus is required, but these sections can be bypassed with no loss of continuity. The major part of the book should therefore be accessible to graduate students so that it can serve as an introduction to complex analysis in one and several variables. The last sections, however, are written mainly for readers familiar with microlocal analysis.

Product Description: Author received the 1962 Fields Medal Author received the 1988 Wolf Prize (honoring achievemnets of a lifetime) Author is leading expert in partial differential equations

Due to popular demand this classic presentation of a vast amount on linear partial differential equations by a consummate master of the subject is now available as a study edition. The main change in this new edition is the inclusion of exercises with answers and hints. That is meant to emphasize that this volume can perfectly serve as a general course in modern analysis on a graduate student level and not only as a beginning of a specialised course in partial differential equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of general interest. As in the revised printing of volume II, a number of minor flaws have also been corrected in this edition. Parallely this edition is still available as volume 256 of the Grundlehren der mathematischen Wissenschaften. "... it is the best now available in print. ... All the theorems are there (among them the Schwartz kernel theorem), and all they have ... proofs." Bulletin of the American Mathematical Society#1 "It certainly will be a classic for many years." Zentralblatt für Mathematik#2

Product Description: 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...read more

Product Description: 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...read more

Product Description: A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the main tool...read more

Product Description: Marcel Riesz (1886-1969) was the younger of the famed pair of mathematicians and brothers. Although Hungarian he spent most of his professional life in Sweden. He worked on summability theory, analytic functions, the moment problem, harmonic and functional analysis, potential theory and the wave equation...read more

Product Description: 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...read more

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 Honours awarded to Lars Hörmander: Fields Medal 1962, Speaker at International Congress 1970, Wolf Prize 1988, AMS Steele Prize 2006

Product Description: From the reviews: "With the basic theory of distributions and Fourier analysis set down, volume II proceeds deeper into the study of linear PDE, particularly with constant coefficients. Detailed analysis is made of the regularity of certain fundamental solutions of general constant coefficient operators P(D), including a classification of when P(D) is hypoelliptic...read more

Product Description: Due to popular demand this classic presentation of a vast amount on linear partial differential equations by a consummate master of the subject is now available as a study edition. The main change in this new edition is the inclusion of exercises with answers and hints...read more

Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.