dc.contributor.author | Guillemin, Victor W | |
dc.contributor.author | Wang, Zuoqin | |
dc.date.accessioned | 2016-10-04T18:07:58Z | |
dc.date.available | 2016-10-04T18:07:58Z | |
dc.date.issued | 2015-12 | |
dc.date.submitted | 2015-04 | |
dc.identifier.issn | 0266-5611 | |
dc.identifier.issn | 1361-6420 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/104646 | |
dc.description.abstract | Let M be a Riemannian manifold, τ : G x M --> M an isometric action on M of an n-torus G and V : M --> R a bounded G-invariant smooth function. By G-invariance the Schrödinger operator, P = -h[superscript 2][Delta]M + V, restricts to a self-adjoint operator on L[superscript 2](M)[subscript alpha over h], alpha being a weight of G and 1[over h] a large positive integer. Let [c[subscript alpha], [infinity]] be the asymptotic support of the spectrum of this operator. We will show that c[subscript alpha] extend to a function, W : g*-->R and that, modulo assumptions on τ and V one can recover V from W, i.e. prove that V is spectrally determined. The main ingredient in the proof of this result is the existence of a 'generalized Legendre transform' mapping the graph of dW onto the graph of dV. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Grant DMS-1005696) | en_US |
dc.description.sponsorship | National Natural Science Foundation (China) (NSFC no. 11571331) | en_US |
dc.language.iso | en_US | |
dc.publisher | Institute of Physics Publishing (IOP) | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1088/0266-5611/32/1/015001 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | arXiv | en_US |
dc.title | The generalized Legendre transform and its applications to inverse spectral problems | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Guillemin, Victor and Zuoqin Wang. "The generalized Legendre transform and its applications to inverse spectral problems." Inverse Problems 32:1 (December 2015), 015001. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Guillemin, Victor W | |
dc.relation.journal | Inverse Problems | en_US |
dc.eprint.version | Original manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/NonPeerReviewed | en_US |
dspace.orderedauthors | Guillemin, Victor; Wang, Zuoqin | en_US |
dspace.embargo.terms | N | en_US |
dc.identifier.orcid | https://orcid.org/0000-0003-2641-1097 | |
mit.license | OPEN_ACCESS_POLICY | en_US |