Ulteriori informazioni
Klappentext Pseudodifferential operators arise naturally in a 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. While a pseudodifferential operator is commonly defined by an integral formula, it also may 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. The Technique of Pseudodifferential Operators will be of particular interest to researchers in partial differential equations and mathematical physics. Zusammenfassung This technique is used in the solution of boundary problems for partial differential equations. Its applications include the Dirac theory of quantum mechanics. The author discusses connections to the theory of C*-algebras and the relation of the hyperbolic theory to the propagation of maximal ideals. Inhaltsverzeichnis 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.
