One-Parameter Semigroups Generated by Strongly M-Elliptic Pseudo-Differential Operators on Euclidean Spaces
| dc.contributor.advisor | Wong, Man Wah | |
| dc.contributor.author | Gao, Yaodong | |
| dc.date.accessioned | 2024-07-18T21:17:19Z | |
| dc.date.available | 2024-07-18T21:17:19Z | |
| dc.date.copyright | 2024-03-18 | |
| dc.date.issued | 2024-07-18 | |
| dc.date.updated | 2024-07-18T21:17:19Z | |
| dc.degree.discipline | Mathematics & Statistics | |
| dc.degree.level | Doctoral | |
| dc.degree.name | PhD - Doctor of Philosophy | |
| dc.description.abstract | We begin with a recall of the definitions and basic properties of the standard Hörmander classes of pseudo-differential operators on Rn. Then we introduce a new class of pseudo-differential operators that can be traced back to Taylor, generalized by Garello and Morando and further developed by M. W. Wong. A related class of pseudo-differential operators depending on a complex parameter on an open subset of the complex plane is constructed. We tease out from this related class the strongly M – elliptic pseudo-differential operators and prove that they are infinitesimal generators of holomorphic and hence strongly continuous one-parameter semigroups of bounded linear operators on Lp(Rn), 1<p<ꚙ. The proof is based on careful refinements of the Agmon – Douglis – Nirenberg estimates for the pseudo-differential operators in the book by M. W. Wong. In the case when p=2, we give another proof that strongly (ρ,Λ) – elliptic pseudo-differential operators, which include strongly M – elliptic ones, are infinitesimal generators of strongly continuous one-parameter semigroups of bounded linear operators on L2(Rn) by first proving Gårding’s Inequality for strongly (ρ,Λ) – elliptic pseudo-differential operators on Rn. | |
| dc.identifier.uri | https://hdl.handle.net/10315/42125 | |
| dc.language | en | |
| dc.rights | Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests. | |
| dc.title | One-Parameter Semigroups Generated by Strongly M-Elliptic Pseudo-Differential Operators on Euclidean Spaces | |
| dc.type | Electronic Thesis or Dissertation |
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