Contents: Contents of Volumes I and III.
- Pseudodifferential Operators.
- Spectral Theory.
- Scattering by Obstacles.
- Dirac Operators and Index Theory.
- Brownian Motion and Potential Theory.
- The Partial-Neumann Problem.
- Connections and Curvature.
Über den Autor
Michael E. Taylor is a Professor at University of North Carolina in the Department of Mathematics.
This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.