dc.contributor.author | Grochenig, Karlheinz | |
dc.contributor.author | Jaming, Philippe | |
dc.contributor.author | Malinnikova, Eugenia | |
dc.date.accessioned | 2020-07-16T10:10:43Z | |
dc.date.available | 2020-07-16T10:10:43Z | |
dc.date.created | 2020-02-01T19:43:13Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Revista Matemática Complutense. 2019, 1-22. | en_US |
dc.identifier.issn | 1139-1138 | |
dc.identifier.uri | https://hdl.handle.net/11250/2669254 | |
dc.description.abstract | We study the question under which conditions the zero set of a (cross-) Wigner distribution W(f, g) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will construct less obvious examples consisting of exponential functions and their convolutions. The results require elements from the theory of totally positive functions, Bessel functions, and Hurwitz polynomials. The question of zero-free Wigner distributions is also related to Hudson’s theorem for the positivity of the Wigner distribution and to Hardy’s uncertainty principle. We then construct a class of step functions S so that the Wigner distribution W(f,1(0,1)) always possesses a zero f∈S∩Lp when p<∞, but may be zero-free for f∈S∩L∞. The examples show that the question of zeros of the Wigner distribution may be quite subtle and relate to several branches of analysis. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer Nature | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Zeros of the Wigner distribution and the short-time Fourier transform | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | publishedVersion | en_US |
dc.source.pagenumber | 1-22 | en_US |
dc.source.journal | Revista Matemática Complutense | en_US |
dc.identifier.doi | 10.1007/s13163-019-00335-w | |
dc.identifier.cristin | 1789657 | |
dc.description.localcode | Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |