A Shubin pseudodifferential calculus on asymptotically conic manifolds
Abstract
We present a global pseudodifferential calculus on asymptotically conic manifolds that generalizes (anisotropic versions of) Shubin's classical global pseudodifferential calculus on Euclidean space to this class of noncompact manifolds. Fully elliptic operators are shown to be Fredholm in an associated scale of Sobolev spaces, and to have parametrices in the calculus.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.08169
- arXiv:
- arXiv:2408.08169
- Bibcode:
- 2024arXiv240808169K
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Functional Analysis;
- Mathematics - Operator Algebras;
- 58J40 (Primary) 58J05;
- 47G30 (Secondary)