Subspaces of L^2(R^n) Invariant Under Crystallographic Shifts
| dc.contributor.author | Potter, Tom | |
| dc.contributor.copyright-release | Not Applicable | |
| dc.contributor.degree | Doctor of Philosophy | |
| dc.contributor.department | Department of Mathematics & Statistics - Math Division | |
| dc.contributor.ethics-approval | Not Applicable | |
| dc.contributor.external-examiner | Dr. Yemon Choi | |
| dc.contributor.manuscripts | Not Applicable | |
| dc.contributor.thesis-reader | Dr. Keith Johnson | |
| dc.contributor.thesis-reader | Dr. Theo Johnson-Freyd | |
| dc.contributor.thesis-supervisor | Dr. Keith Taylor | |
| dc.date.accessioned | 2025-10-14T16:47:12Z | |
| dc.date.available | 2025-10-14T16:47:12Z | |
| dc.date.defence | 2025-09-29 | |
| dc.date.issued | 2025-10-14 | |
| dc.description.abstract | In this thesis we consider crystal groups in dimension n and their natural unitary representation on L^2(R^n). We show that this representation is unitarily equivalent to a direct integral of factor representations, and use this to characterize the subspaces of L^2(R^n) invariant under crystal symmetry shifts. Finally, by giving an explicit unitary equivalence of the natural crystal group representation, we find the central decomposition guaranteed by direct integral theory. | |
| dc.identifier.uri | https://hdl.handle.net/10222/85472 | |
| dc.language.iso | en | |
| dc.subject | crystallographic groups | |
| dc.subject | crystal symmetry shifts | |
| dc.subject | central decomposition | |
| dc.subject | direct integral theory | |
| dc.subject | unitary representation | |
| dc.title | Subspaces of L^2(R^n) Invariant Under Crystallographic Shifts |