The Technique of Pseudodifferential Operators

Erscheinungsjahr 2008
ISBN: 978-0-521-37864-2
Verlag: Cambridge University Press

Buch, Englisch, Band 202, 394 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 641 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Codes, H. O.

Cordes, H. O.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

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.