The Analysis of Linear Partial Differential Operators III: Pseudo-Differential Operators

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Springer Science & Business Media, 23.12.1994 - 525 Seiten

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.

 

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Ausgewählte Seiten

Inhalt

Second Order Elliptic Operators Summary
3
171 Interior Regularity and Local Existence Theorems
4
172 Unique Continuation Theorems
9
173 The Dirichlet Problem
24
174 The Hadamard Parametrix Construction
30
175 Asymptotic Properties of Eigenvalues and Eigenfunctions
42
Notes
61
PseudoDifferential Operators
63
Notes
346
Some Classes of MicroHypoelliptic Operators
348
221 Operators With PseudoDifferential Parametrix
349
222 Generalized Kolmogorov Equations
353
223 Melins Inequality
359
224 Hypoellipticity with Loss of One Derivative
366
Notes
383
The Strictly Hyperbolic Cauchy Problem
385

181 The Basic Calculus
65
182 Conormal Distributions
96
183 Totally Characteristic Operators
112
184 Gauss Transforms Revisited
141
185 The Weyl Calculus
150
186 Estimates of PseudoDifferential Operators
161
Notes
178
Elliptic Operators on a Compact Manifold Without Boundary
180
192 The Index of Elliptic Operators
193
193 The Index Theorem in IR
215
194 The Lefschetz Formula
222
195 Miscellaneous Remarks on Ellipticity
225
Notes
229
Boundary Problems for Elliptic Differential Operators
231
201 Elliptic Boundary Problems
232
202 Preliminaries on Ordinary Differential Operators
251
203 The Index for Elliptic Boundary Problems
255
204 NonElliptic Boundary Problems
264
Notes
266
Symplectic Geometry
268
211 The Basic Structure
269
212 Submanifolds of a Symplectic Manifold
283
213 Normal Forms of Functions
296
214 Folds and Glancing Hypersurfaces
303
215 Symplectic Equivalence of Quadratic Forms
321
216 The Lagrangian Grassmannian
328
232 Operators of Higher Order
390
233 Necessary Conditions for Correctness of the Cauchy Problem
400
234 Hyperbolic Operators of Principal Type
404
Notes
414
The Mixed DirichletCauchy Problem for Second Order Operators
416
242 Singularities in the Elliptic and Hyperbolic Regions
423
243 The Generalized Bicharacteristic Flow
430
244 The Diffractive Case
443
245 The General Propagation of Singularities
455
246 Operators Microlocally of Tricomis Type
460
247 Operators Depending on Parameters
465
Notes
469
Appendix B Some Spaces of Distributions
471
B2 Distributions in a Half Space and in a Manifold with Boundary
478
Appendix C Some Tools from Differential Geometry
485
C2 A Singular Differential Equation
487
C3 Clean Intersections and Maps of Constant Rank
490
C4 Folds and Involutions
492
C5 Geodesic Normal Coordinates
500
C6 The Morse Lemma with Parameters
502
Notes
504
Bibliography
505
Index
523
Index of Notation
Urheberrecht

Häufige Begriffe und Wortgruppen

Beliebte Passagen

Seite 519 - Schapira, P. Propagation at the boundary and reflection of analytic singularities of solutions of linear partial differential equations. Publ. RIMS Kyoto Univ.
Seite 521 - Introduction to Pseudodifferential and Fourier Integral Operators, Volume 1: Pseudodifferential Operators, Volume 2: Fourier Integral Operators, by Francois Treves; Plenum Press, New York, 1980; 649 pages, $29.95 & 35.00, cloth.
Seite 512 - On surface waves with finite and infinite speed of propagation, Arch. Rational Mech. Anal. 19 (1965).

Über den Autor (1994)

Biography 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. 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.

Bibliografische Informationen