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
Author(s): Lars Hörmander
Series: Grundlehren der mathematischen Wissenschaften
Edition: 1
Publisher: Springer
Year: 2009
Language: English
Commentary: This version has OCR, a complete PDF table of contents, and is more compact than previous PDF versions
Pages: 352
City: Berlin, Heidelberg
Front Cover
Preface
Contents
Chapter XXV. Lagrangian Distributions and Fourier Integral Operators
Summary
25.1. Lagrangian Distributions
25.2. The Calculus of Fourier Integral Operators
25.3. Special Cases of the Calculus, and ?² Continuity
25.4. Distributions Associated with Positive Lagrangian Ideals
25.5. Fourier Integral Operators with Complex Phase
Notes
Chapter XXVI. Pseudo-Differential Operators of Principal Type
Summary
26.1. Operators
26.2. The Complex Involutive Case
26.3. The Symplectic Case
26.4. Solvability and Condition (?)
26.5. Geometrical Aspects of Condition (?)
26.6. The Singularities in ?₁₁
26.7. Degenerate Cauchy-Riemann Operators
26.10. The Singularities on One Dimensional Bicharacteristics
26.11. A Semi-Global Existence Theorem
Chapter XXVII. Subelliptic Operators
Summary
27.1. Definitionsand Main Results
27.2. Tbe Taylor Expansion of the Symbol
27.3. Subelliptic Operators Satisfying (?)
27.4. Local Properties of the Symbol
27.5. Local Subelliptic Estimates
Subelliptic Estimates
27.6. Global Subelliptic Estimates
Notes
Chapter XXVIII. Uniqueness for the Cauchy Problem
Summary
28.1. Calderón's Uniqueness Theorem
28.2. General Carleman Estimates
28.3. Uniqueness Under Convexity Conditions
28.4. Second Order Operators of Real Principal Type
Notes
Chapter XXIX. Spectral Asymptotics
Summary
29.1. The Spectral Measure and its Fourier Transform
29.2. The Case of a Periodic Hamitton Flow
29.3. The Weyl Forrnula for the Dirichlet Problern
Notes
Chapter XXX. Long Range Scattering Theory
Summary
30.1. Admissible Perturbations
30.2 The Boundary Value of the Resolvent, and the Point Spectrum
30.3. The Hamilton Flow
30.4. Modified Wave Operators
30.5. Distorted Fourier Transforms and Asymptotic Completeness
Notes
Bibliography
Index
Index of Notation
