{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T17:38:32Z","timestamp":1780335512500,"version":"3.54.1"},"reference-count":45,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,31]],"date-time":"2020-12-31T00:00:00Z","timestamp":1609372800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","doi-asserted-by":"publisher","award":["19-19535S"],"award-info":[{"award-number":["19-19535S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Explicit links of the multivariate discrete (anti)symmetric cosine and sine transforms with the generalized dual-root lattice Fourier\u2013Weyl transforms are constructed. Exact identities between the (anti)symmetric trigonometric functions and Weyl orbit functions of the crystallographic root systems A1 and Cn are utilized to connect the kernels of the discrete transforms. The point and label sets of the 32 discrete (anti)symmetric trigonometric transforms are expressed as fragments of the rescaled dual root and weight lattices inside the closures of Weyl alcoves. A case-by-case analysis of the inherent extended Coxeter\u2013Dynkin diagrams specifically relates the weight and normalization functions of the discrete transforms. The resulting unique coupling of the transforms is achieved by detailing a common form of the associated unitary transform matrices. The direct evaluation of the corresponding unitary transform matrices is exemplified for several cases of the bivariate transforms.<\/jats:p>","DOI":"10.3390\/sym13010061","type":"journal-article","created":{"date-parts":[[2020,12,31]],"date-time":"2020-12-31T14:31:49Z","timestamp":1609425109000},"page":"61","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Connecting (Anti)Symmetric Trigonometric Transforms to Dual-Root Lattice Fourier\u2013Weyl Transforms"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0271-1095","authenticated-orcid":false,"given":"Adam","family":"Brus","sequence":"first","affiliation":[{"name":"Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Prague, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8501-971X","authenticated-orcid":false,"given":"Ji\u0159\u00ed","family":"Hrivn\u00e1k","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Prague, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6174-0518","authenticated-orcid":false,"given":"Lenka","family":"Motlochov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Prague, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"093504","DOI":"10.1063\/1.2779768","article-title":"(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms","volume":"48","author":"Klimyk","year":"2007","journal-title":"J. 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