On the Existence and Structure of Ψ*-Algebras of Totally Characteristic Operators on Compact Manifolds with Boundary
✍ Scribed by Robert Lauter
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 575 KB
- Volume
- 169
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
As a contribution to the pseudodifferential analysis on manifolds with singularities we construct for each smooth, compact manifold X with boundary a 9*-algebra
) of totally characteristic pseudodifferential operators introduced by Melrose [25] in 1981 as a dense subalgebra; further, there is a homomorphism
9 is an algebra of C -symbols reflecting the smooth structure of the manifold X. The Fredholm inverses of Fredholm operators in A (b) (X, b 0 1Â2 ) are again in the algebra A (b) (X, r 0 1Â2 ), and we have elliptic regularity corresponding to the scale * b H m b (X, b 0 1Â2 ) of b-Sobolev spaces naturally associated to X. Localized to the interior of X we recover the ordinary pseudodifferential calculus. Finally, spectrum, Jacobson topology and the relationship of certain closed ideals in the algebra A (b) (X, b 0 1Â2 ) are described explicitly.