{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T04:04:29Z","timestamp":1778040269607,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T00:00:00Z","timestamp":1665705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004410","name":"TUBITAK Research","doi-asserted-by":"publisher","award":["120F140"],"award-info":[{"award-number":["120F140"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004410","name":"TUBITAK Research","doi-asserted-by":"publisher","award":["PID2020-113275GB-I00"],"award-info":[{"award-number":["PID2020-113275GB-I00"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n (AEI) of Spain","doi-asserted-by":"publisher","award":["120F140"],"award-info":[{"award-number":["120F140"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n (AEI) of Spain","doi-asserted-by":"publisher","award":["PID2020-113275GB-I00"],"award-info":[{"award-number":["PID2020-113275GB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Community fund FEDER","award":["120F140"],"award-info":[{"award-number":["120F140"]}]},{"name":"European Community fund FEDER","award":["PID2020-113275GB-I00"],"award-info":[{"award-number":["PID2020-113275GB-I00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Some systems of univariate orthogonal polynomials can be mapped into other families by the Fourier transform. The most-studied example is related to the Hermite functions, which are eigenfunctions of the Fourier transform. For the multivariate case, by using the Fourier transform and Parseval\u2019s identity, very recently, some examples of orthogonal systems of this type have been introduced and orthogonality relations have been discussed. In the present paper, this method is applied for multivariate orthogonal polynomials on the unit ball. The Fourier transform of these orthogonal polynomials on the unit ball is obtained. By Parseval\u2019s identity, a new family of multivariate orthogonal functions is introduced. The results are expressed in terms of the continuous Hahn polynomials.<\/jats:p>","DOI":"10.3390\/axioms11100558","type":"journal-article","created":{"date-parts":[[2022,10,16]],"date-time":"2022-10-16T21:10:10Z","timestamp":1665954610000},"page":"558","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Fourier Transform of the Orthogonal Polynomials on the Unit Ball and Continuous Hahn Polynomials"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7653-8745","authenticated-orcid":false,"given":"Esra","family":"G\u00fcldo\u011fan Lekesiz","sequence":"first","affiliation":[{"name":"Faculty of Engineering, Ostim Technical University, Ankara 06374, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7811-8610","authenticated-orcid":false,"given":"Rabia","family":"Akta\u015f","sequence":"additional","affiliation":[{"name":"Faculty of Science, Department of Mathematics, Ankara University, Ankara 06100, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0872-5017","authenticated-orcid":false,"given":"Iv\u00e1n","family":"Area","sequence":"additional","affiliation":[{"name":"CITMAga, Departamento de Matem\u00e1tica Aplicada II, Universidade de Vigo, E. 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