The Technique of Pseudodifferential Operators

ISBN-13: 9780521378642 / Angielski / Miękka / 1995 / 396 str.

H. O. Codes; H. O. Cordes

Opis

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.

Recenzje

"...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

Spis treści

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.