| dc.contributor.author | Pritsker, Igor E | |
| dc.date.accessioned | 2024-01-17T19:55:08Z | |
| dc.date.available | 2024-01-17T19:55:08Z | |
| dc.date.issued | 2013-07-20 | |
| dc.identifier | oksd_pritsker_how_to_find_a_2013 | |
| dc.identifier.citation | Pritsker, I.E. (2013). How to find a measure from its potential. https://doi.org/10.48550/arxiv.1307.5457 | |
| dc.identifier.uri | https://hdl.handle.net/11244/340126 | |
| dc.description.abstract | We consider the problem of finding a measure from the given values of its logarithmic potential on the support. It is well known that a solution to this problem is given by the generalized Laplacian. The case of our main interest is when the support is contained in a rectifiable curve, and the measure is absolutely continuous with respect to the arclength on this curve. Then the generalized Laplacian is expressed by a sum of normal derivatives of the potential. Such representation was available for smooth curves, and we show it holds for any rectifiable curve in the plane. We also relax the assumptions imposed on the potential. | |
| dc.description.abstract | Finding a measure from its potential often leads to another closely related problem of solving a singular integral equation with Cauchy kernel. The theory of such equations is well developed for smooth curves. We generalize this theory to the class of Ahlfors regular curves and arcs, and characterize the bounded solutions on arcs. | |
| dc.format | application/pdf | |
| dc.language | en_US | |
| dc.rights | This material has been previously published. In the Oklahoma State University Library's institutional repository this version is made available through the open access principles and the terms of agreement/consent between the author(s) and the publisher. The permission policy on the use, reproduction or distribution of the material falls under fair use for educational, scholarship, and research purposes. Contact Digital Resources and Discovery Services at lib-dls@okstate.edu or 405-744-9161 for further information. | |
| dc.title | How to find a measure from its potential | |
| dc.date.updated | 2024-01-16T23:28:28Z | |
| osu.filename | oksd_pritsker_how_to_find_a_2013.pdf | |
| dc.identifier.doi | 10.48550/arxiv.1307.5457 | |
| dc.description.department | Mathematics | |
| dc.type.genre | Preprint | |
| dc.type.material | Text | |
| dc.subject.keywords | applied mathematics | |
| dc.subject.keywords | pure mathematics | |
| dc.subject.keywords | mathematical sciences | |
| dc.identifier.author | ORCID: 0000-0002-3102-5003 (Pritsker, Igor E) | |
| dc.identifier.author | ScopusID: 6602900239 (Pritsker, Igor E) | |
