{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T17:49:20Z","timestamp":1776275360538,"version":"3.50.1"},"reference-count":26,"publisher":"American Mathematical Society (AMS)","issue":"8","license":[{"start":{"date-parts":[[2011,4,15]],"date-time":"2011-04-15T00:00:00Z","timestamp":1302825600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>\n                    We define an analogue of the Paley-Wiener space in the context of the Askey-Wilson function transform, compute explicitly its reproducing kernel and prove that the growth of functions in this space of entire functions is of order two and type\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"ln q Superscript negative 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>ln<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>q<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2212\n                                  \n                                <\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\ln q^{-1}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , providing a Paley-Wiener Theorem for the Askey-Wilson transform. Up to a change of scale, this growth is related to the refined concepts of exponential order and growth proposed by J. P. Ramis. The Paley-Wiener theorem is proved by combining a sampling theorem with a result on interpolation of entire functions due to M. E. H. Ismail and D.\u00a0Stanton.\n                  <\/p>","DOI":"10.1090\/s0002-9939-10-10327-x","type":"journal-article","created":{"date-parts":[[2010,4,29]],"date-time":"2010-04-29T11:02:04Z","timestamp":1272538924000},"page":"2853-2862","source":"Crossref","is-referenced-by-count":10,"special_numbering":"614","title":["A Paley-Wiener theorem for the Askey-Wilson function transform"],"prefix":"10.1090","volume":"138","author":[{"given":"Lu\u00eds","family":"Abreu","sequence":"first","affiliation":[]},{"given":"Fethi","family":"Bouzeffour","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2010,4,15]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"1197","DOI":"10.1090\/S0002-9939-04-07589-6","article-title":"A \ud835\udc5e-sampling theorem related to the \ud835\udc5e-Hankel transform","volume":"133","author":"Abreu, L. D.","year":"2005","journal-title":"Proc. Amer. Math. 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