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In particular we show that the sets of Wigner functions on distinct symplectic spaces are different but have non-empty intersections. This extends previous results to arbitrary dimension and arbitrary (constant) symplectic structure. As a by-product we introduce and prove several concepts and results on non-standard symplectic spaces which generalize those on the standard symplectic space, namely, the symplectic spectrum, Williamson\u2019s theorem, and Narcowich-Wigner spectra. We also show how Wigner functions on non-standard symplectic spaces behave under the action of an arbitrary linear coordinate transformation.<\/jats:p>","DOI":"10.1063\/1.5001069","type":"journal-article","created":{"date-parts":[[2018,1,24]],"date-time":"2018-01-24T14:53:17Z","timestamp":1516805597000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Wigner functions on non-standard symplectic vector spaces"],"prefix":"10.1063","volume":"59","author":[{"given":"Nuno Costa","family":"Dias","sequence":"first","affiliation":[{"name":"Grupo de F\u00edsica Matem\u00e1tica, Departamento de Matem\u00e1tica, Universidade de Lisboa , Edif\u00edcio C6, Ave. Campo Grande, 1749-016 Lisboa, Portugal"}]},{"given":"Jo\u00e3o Nuno","family":"Prata","sequence":"additional","affiliation":[{"name":"Grupo de F\u00edsica Matem\u00e1tica, Departamento de Matem\u00e1tica, Universidade de Lisboa , Edif\u00edcio C6, Ave. Campo Grande, 1749-016 Lisboa, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2018,1,24]]},"reference":[{"key":"2023070516042319000_c1","doi-asserted-by":"publisher","first-page":"1710","DOI":"10.1364\/josa.69.001710","article-title":"Wigner distribution function and its application to first order optics","volume":"69","year":"1979","journal-title":"J. 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