Spectral Theory of Linear Differential Operators and Comparison Algebras

The main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators.

Heinz Otto Cordes (Author)

9780521284431, Cambridge University Press

Paperback, published 23 April 1987

356 pages
22.8 x 15.2 x 2 cm, 0.52 kg

The main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators. The first part of the book develops the necessary elements of the spectral theory of differential operators as well as the basic properties of elliptic second order differential operators. The author then introduces comparison algebras and describes their theory in L2-spaces and L2-Soboler spaces, and in particular their importance in solving functional analytic problems involving differential operators. The book is based on lectures given in Sweden and the USA.

1. Abstract spectral theory in Hilbert spaces
2. Spectral theory of differential operators
3. Second order elliptic expressions on manifolds
4. Essential self-adjointness of the Minimal Operator
5. C -Comparison algebras
6. Minimal comparison algebra and wave front space
7. The secondary symbol space
8. Comparison algebras with non-compact commutators
9. Hs-Algebras: higher order operators within reach
10. Fredholm theory in comparison algebras

Subject Areas: Probability & statistics [PBT]