In this work we present a symbolic calculus for ΨDOs on a smooth manifold M based on a suitable notion of the global phase function. In previous literature on the topic, either local coordinates or connections have been used to define the phase functions, symbols and oscillatory integrals defining ΨDOs. We obtain global formulae for the compositions and adjoints of ΨDOs. Applications are given to elliptic ΨDOs, boundedness on Sobolev spaces and functional calculus for elliptic ΨDOs.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:686369 |
| Date | January 2015 |
| Creators | Battistotti, Paolo |
| Contributors | Safarov, Yuri |
| Publisher | King's College London (University of London) |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://kclpure.kcl.ac.uk/portal/en/theses/an-invariant-approach-to-symbolic-calclus-foe-pseudodifferential-operators-on-manifolds(228c33cf-d786-4796-8f42-5835881bc7fa).html |
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