Pseudodifferential Operators

PSEUDODIFFERENTIAL OPERATORS Here Michael Taylor develops pseudodifferential operators as a tool for treating problems in linear partial differential equations, including existence, uniqueness, and estimates of smoothness, as well as other qualitative properties. In addition, he treats solutions to initial and boundary value problems that arise in mathematical physics and in pure mathematics. He also develops the theory of Fourier integral operators and the theory of geometrical optics, including a study of the diffraction of waves, and a study of transformation of operators to standard forms. To put in perspective the role of pseudodifferential operators in the study of linear partial differential equations, the author discusses the interplay between · functional analysis, Fourier analysis, energy estimates, and fundamental solutions and parametrices. The first fourteen chapters deal primarily with operators that are either elliptic or whose characteristics are simple. The final chapter studies operators with double characteristics. Michael E. Taylor is Professor of Mathematics at Rice University. Princeton Mathematical Series, 34 Pseudodijferential Operators PRINCETON MATHEMATICAL SERIES Editors: WU-CHUNG HSIANG, ROBERT P. LANGLANDS, JOHN D. MILNOR, and ELIAS M. STEIN 1. 3. 4. 6. 7. 8. 9. 10. 11. 12. 14. 15. 16. 17. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. The Classical Groups, By HERMAN WEYL An Introduction to Differential Geometry, By LUTHER PFAHLER EISENHART Dimension Theory, ByW. HUREWICZ and H. WALLMAN The Laplace Transform, By D. V. WIDDER Integration, By EDw ARD J. MCSHANE Theory of Lie Groups: 1, By C. CHEV ALLEY Mathematical Methods of Statistics, By HARALD CRAMER Several Complex Variables, By S. BOCHNER and W. T. MARTIN Introduction to Topology, By S. LEFSCHETZ Algebraic Geometry and Topology, edited by R. H. Fox, D. C. SPENCER, and A. W. TUCKER The Topology of Fibre Bundles, By NORMAN STEENROD Foundations of Algebraic Topology, By SAMUEL EILENBERG and NORMAN STEENROD Functionals of Finite Riemann Surfaces, By MENAHEM SCHIFFER and DONALD C. SPENCER. Introduction to Mathematical Logic, Vol. 1, By ALONZO CHURCH Homological Algebra, By H. CARTAN and S. EILENBERG The Convolution Transform, By I. I. HIRSCHMAN and D. V. WIDDER Geometric Integration Theory, By H. WHITNEY Qualitative Theory of Differential Equations, By V. V. NEMYTSKII and V. V. STEPANOV Topological Analysis, By GORDON T. WHYBURN (revised 1964) Analytic Functions, By AHLFORS, BEHNKE and GRAVERT, BERS, et al. Continuous Geometry, By JOHN VON NEUMANN RIEMANN Surfaces, By L. AHLFORS and L. SARIO Differential and Combinatorial Topology, edited By S. S. CAIRNS Convex Analysis, By R. T. ROCKAFELLAR Global Analysis, edited By D. C. SPENCER and S. IYANAGA Singular Integrals and Differentiability Properties of Functions, By E. M. STEIN Problems in Analysis, edited By R. C. GUNNING Introduction to Fourier Analysis on Euclidean Spaces, By E. M. STEIN and G. WEISS Etale Cohomology, By J. S. MILNE Pseudodifferential Operators, By MICHAEL E. TAYLOR Pseudodifferential Operators Michael E. Taylor PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY Copyright© 1981 by Princeton University Press Published by Princeton University Press, Princeton, New Jersey In the United Kingdom: Princeton University Press, Guildford, Surrey ALL RIGHTS RESERVED Library of Congress Cataloging in Publication Data will be found on the last printed page of this book This book has been composed in Monophoto Times Roman Clothbound editions of Princeton University Press books are printed on acid-free paper, and binding materials are chosen for strength and durability Printed in the United States of America by Princeton University Press, Princeton, New Jersey To Lillian Harden and Sarah Richbourg.