2000
Refine
Has Fulltext
- yes (23)
Year of publication
- 2000 (23)
Document Type
- Preprint (23)
Language
- English (23)
Is part of the Bibliography
- no (23)
Keywords
- K-theory (3)
- elliptic operators (2)
- linking coefficients (2)
- Atiyah-Bott condition (1)
- Atiyah-Patodi-Singer theory (1)
- Crack theory (1)
- Dirac operators (1)
- Fredholm property (1)
- Pontrjagin duality (1)
- conormal asymptotics (1)
- elliptic operators in subspaces (1)
- elliptic operators on non-compact manifolds (1)
- eta invariant (1)
- eta-invariant (1)
- index (1)
- index theory (1)
- manifold with singularities (1)
- modulo n index (1)
- operator algebras on manifolds with singularities (1)
- parity conditions (1)
- problem of classification (1)
- pseudo-differential boundary value problems (1)
- pseudo-differentialboundary value problems (1)
- pseudodifferential subspaces (1)
- relative index (1)
- spectral flow (1)
- surgery (1)
Institute
We prove the existence of Hp(D)-limit of iterations of double layer potentials constructed with the use of Hodge parametrix on a smooth compact manifold X, D being an open connected subset of X. This limit gives us an orthogonal projection from Sobolev space Hp(D) to a closed subspace of Hp(D)-solutions of an elliptic operator P of order p ≥ 1. Using this result we obtain formulae for Sobolev solutions to the equation Pu = f in D whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of double layer potentials. Similar regularization is constructed also for a P-Neumann problem in D.