The Technique of Pseudodifferential Operators

A technique used in the theory of partial differential equations with applications to quantum mechanics.

H. O. Cordes (Author)

9780521378642, Cambridge University Press

Paperback, published 23 February 1995

396 pages
22.8 x 15.2 x 2.1 cm, 0.545 kg

"...interesting and appropriate as a text for an introductory graduate course...it reflects the author's originality and experience in graduate teaching." Alexander Dynin, Bulletin of the American Mathematical Society

Pseudodifferential operators arise naturally in the solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. A pseudodifferential operator may also be described by invariance under action of a Lie-group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution and the relation of the hyperbolic theory to the propagation of maximal ideals. This book will be of particular interest to researchers in partial differential equations and mathematical physics.

Introductory discussion
1. Calculus of pseudodifferential operators
2. Elliptic operators and parametrices in Rn
3. L2-Sobolev theory and applications
4. Pseudodifferential operators on manifolds with conical ends
5. Elliptic and parabolic problems
6. Hyperbolic first order systems on Rn
7. Hyperbolic differential equations
8. Pseudodifferential operators as smooth operators of L(H)
9. Particle flow and invariant algebra of a strictly hyperbolic system
10. The invariant algebra of the Dirac equation.

Subject Areas: Calculus & mathematical analysis [PBK]