{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T10:08:00Z","timestamp":1769249280481,"version":"3.49.0"},"reference-count":24,"publisher":"Walter de Gruyter GmbH","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider a very global <jats:italic>q<\/jats:italic>-integral transform, essentially characterized by having a bounded kernel and satisfying a set of natural and useful properties for the realization of applications. The main ambition of this work is to seek conditions that guarantee uncertainty principles of the Donoho\u2013Stark type for that class of <jats:italic>q<\/jats:italic>-integral transforms. It should be noted that the global character of the <jats:italic>q<\/jats:italic>-integral transform in question allows one to immediately deduce corresponding Donoho\u2013Stark uncertainty principles for <jats:italic>q<\/jats:italic>-integral operators that are its particular cases. These particular cases are very well-known operators, namely: a <jats:italic>q<\/jats:italic>-cosine-Fourier transform, a <jats:italic>q<\/jats:italic>-sine-Fourier transform, a <jats:italic>q<\/jats:italic>-Fourier transform, a <jats:italic>q<\/jats:italic>-Bessel\u2013Fourier transform and a <jats:italic>q<\/jats:italic>-Dunkl transform.\nMoreover, generalizations of the local uncertainty principle of Price for the <jats:italic>q<\/jats:italic>-cosine-Fourier transform, <jats:italic>q<\/jats:italic>-sine-Fourier transform, <jats:italic>q<\/jats:italic>-Fourier transform, <jats:italic>q<\/jats:italic>-Bessel\u2013Fourier transform and <jats:italic>q<\/jats:italic>-Dunkl transform are also obtained.<\/jats:p>","DOI":"10.1515\/forum-2023-0244","type":"journal-article","created":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T11:21:36Z","timestamp":1704108096000},"page":"1359-1381","source":"Crossref","is-referenced-by-count":2,"title":["Donoho\u2013Stark and Price uncertainty principles for a class of <i>q<\/i>-integral transforms with bounded kernels"],"prefix":"10.1515","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4261-8699","authenticated-orcid":false,"given":"Luis P.","family":"Castro","sequence":"first","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA) , Department of Mathematics , University of Aveiro , Aveiro , Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5821-4843","authenticated-orcid":false,"given":"Rita C.","family":"Guerra","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA) , Department of Mathematics , University of Aveiro , Aveiro ; and Coimbra Business School, Polytechnic Institute of Coimbra, Coimbra , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2024,1,2]]},"reference":[{"key":"2024082213230353089_j_forum-2023-0244_ref_001","doi-asserted-by":"crossref","unstructured":"A.  Achak, A.  Abouelaz, R.  Daher and N.  Safouane,\nQuantitative uncertainty principles related to Lions transform,\nArnold Math. J. 8 (2022), no. 3\u20134, 481\u2013496.","DOI":"10.1007\/s40598-022-00202-5"},{"key":"2024082213230353089_j_forum-2023-0244_ref_002","unstructured":"N.  Bettaibi,\nUncertainty principles in \n                  \n                     \n                        \n                           q\n                           2\n                        \n                     \n                     \n                     q^{2}\n                  \n               -analogue Fourier analysis,\nMath. Sci. Res. J. 11 (2007), no. 11, 590\u2013602."},{"key":"2024082213230353089_j_forum-2023-0244_ref_003","unstructured":"N.  Bettaibi and R.  Bettaieb,\nq-analogue of the Dunkl transform on the real line,\nTamsui Oxf. J. Math. Sci. 25 (2009), no. 2, 177\u2013205."},{"key":"2024082213230353089_j_forum-2023-0244_ref_004","doi-asserted-by":"crossref","unstructured":"P.  Boggiatto, E.  Carypis and A.  Oliaro,\nTwo aspects of the Donoho\u2013Stark uncertainty principle,\nJ. Math. Anal. Appl. 434 (2016), no. 2, 1489\u20131503.","DOI":"10.1016\/j.jmaa.2015.09.068"},{"key":"2024082213230353089_j_forum-2023-0244_ref_005","unstructured":"K.  Brahim and B.  Anis,\nOn uncertainty principle of orthonormal sequences for the q-Dunkl transform,\nPolitehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 80 (2018), no. 1, 25\u201332."},{"key":"2024082213230353089_j_forum-2023-0244_ref_006","unstructured":"L.  Dhaouadi, A.  Fitouhi and J.  El Kamel,\nInequalities in q-Fourier analysis,\nJIPAM. J. Inequal. Pure Appl. Math. 7 (2006), no. 5, Article ID 171."},{"key":"2024082213230353089_j_forum-2023-0244_ref_007","doi-asserted-by":"crossref","unstructured":"D. L.  Donoho and P. B.  Stark,\nUncertainty principles and signal recovery,\nSIAM J. Appl. Math. 49 (1989), no. 3, 906\u2013931.","DOI":"10.1137\/0149053"},{"key":"2024082213230353089_j_forum-2023-0244_ref_008","doi-asserted-by":"crossref","unstructured":"D. L.  Donoho and P. B.  Stark,\nA note on rearrangements, spectral concentration, and the zero-order prolate spheroidal wavefunction,\nIEEE Trans. Inform. Theory 39 (1993), no. 1, 257\u2013260.","DOI":"10.1109\/18.179370"},{"key":"2024082213230353089_j_forum-2023-0244_ref_009","doi-asserted-by":"crossref","unstructured":"W. G.  Faris,\nInequalities and uncertainty principles,\nJ. Math. Phys. 19 (1978), no. 2, 461\u2013466.","DOI":"10.1063\/1.523667"},{"key":"2024082213230353089_j_forum-2023-0244_ref_010","doi-asserted-by":"crossref","unstructured":"A.  Fitouhi, N.  Bettaibi and R. H.  Bettaieb,\nOn Hardy\u2019s inequality for symmetric integral transforms and analogous,\nAppl. Math. Comput. 198 (2008), no. 1, 346\u2013354.","DOI":"10.1016\/j.amc.2007.08.040"},{"key":"2024082213230353089_j_forum-2023-0244_ref_011","unstructured":"A.  Fitouhi, F.  Nouri and S.  Guesmi,\nOn Heisenberg and local uncertainty principles for the q-Dunkl transform,\nJIPAM. J. Inequal. Pure Appl. Math. 10 (2009), no. 2, Article ID 42."},{"key":"2024082213230353089_j_forum-2023-0244_ref_012","unstructured":"G.  Gasper and M.  Rahman,\nBasic Hypergeometric Series,\nEncyclopedia Math. Appl. 35,\nCambridge University, Cambridge, 1990."},{"key":"2024082213230353089_j_forum-2023-0244_ref_013","doi-asserted-by":"crossref","unstructured":"M.  Hleili, B.  Nefzi and A.  Bsaissa,\nA variation on uncertainty principles for the generalized q-Bessel Fourier transform,\nJ. Math. Anal. Appl. 440 (2016), no. 2, 823\u2013832.","DOI":"10.1016\/j.jmaa.2016.03.053"},{"key":"2024082213230353089_j_forum-2023-0244_ref_014","doi-asserted-by":"crossref","unstructured":"V.  Kac and P.  Cheung,\nQuantum Calculus,\nUniversitext,\nSpringer, New York, 2002.","DOI":"10.1007\/978-1-4613-0071-7"},{"key":"2024082213230353089_j_forum-2023-0244_ref_015","doi-asserted-by":"crossref","unstructured":"T. H.  Koornwinder and R. F.  Swarttouw,\nOn q-analogues of the Fourier and Hankel transforms,\nTrans. Amer. Math. Soc. 333 (1992), no. 1, 445\u2013461.","DOI":"10.1090\/S0002-9947-1992-1069750-0"},{"key":"2024082213230353089_j_forum-2023-0244_ref_016","doi-asserted-by":"crossref","unstructured":"B.  Nefzi,\nUncertainty principles for the q-Bessel Fourier transform,\nIntegral Transforms Spec. Funct. 30 (2019), no. 11, 920\u2013939.","DOI":"10.1080\/10652469.2019.1636374"},{"key":"2024082213230353089_j_forum-2023-0244_ref_017","doi-asserted-by":"crossref","unstructured":"B.  Nefzi,\nA variation of the \n                  \n                     \n                        \n                           \u2112\n                           \n                              q\n                              ;\n                              p\n                           \n                        \n                     \n                     \n                     \\mathcal{L}_{q;p}\n                  \n               -uncertainty inequalities of Heisenberg-type for symmetric q-integral transforms,\nMath. Methods Appl. Sci. 45 (2022), 5839\u20135863.","DOI":"10.1002\/mma.8143"},{"key":"2024082213230353089_j_forum-2023-0244_ref_018","doi-asserted-by":"crossref","unstructured":"B.  Nefzi and K.  Brahim,\nCalder\u00f3n\u2019s reproducing formula and uncertainty principle for the continuous wavelet transform associated with the q-Bessel operator,\nJ. Pseudo-Differ. Oper. Appl. 9 (2018), no. 3, 495\u2013522.","DOI":"10.1007\/s11868-017-0209-9"},{"key":"2024082213230353089_j_forum-2023-0244_ref_019","unstructured":"A.  Nemri,\nq-Donoho\u2013Stark\u2019s uncertainty principle and q-Tikhonov regularization problem,\nPolitehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 81 (2019), no. 1, 81\u201392."},{"key":"2024082213230353089_j_forum-2023-0244_ref_020","doi-asserted-by":"crossref","unstructured":"J. F.  Price,\nInequalities and local uncertainty principles,\nJ. Math. Phys. 24 (1983), no. 7, 1711\u20131714.","DOI":"10.1063\/1.525916"},{"key":"2024082213230353089_j_forum-2023-0244_ref_021","doi-asserted-by":"crossref","unstructured":"J. F.  Price,\nSharp local uncertainty inequalities,\nStudia Math. 85 (1987), no. 1, 37\u201345.","DOI":"10.4064\/sm-85-1-37-45"},{"key":"2024082213230353089_j_forum-2023-0244_ref_022","doi-asserted-by":"crossref","unstructured":"R. L.  Rubin,\nDuhamel solutions of non-homogeneous \n                  \n                     \n                        \n                           q\n                           2\n                        \n                     \n                     \n                     q^{2}\n                  \n               -analogue wave equations,\nProc. Amer. Math. Soc. 135 (2007), no. 3, 777\u2013785.","DOI":"10.1090\/S0002-9939-06-08525-X"},{"key":"2024082213230353089_j_forum-2023-0244_ref_023","unstructured":"A.  Saoudi,\nUncertainty principle for the Fourier-like multipliers operators in q-Rubin setting,\nBull. Math. Anal. Appl. 14 (2022), no. 1, 1\u201310."},{"key":"2024082213230353089_j_forum-2023-0244_ref_024","doi-asserted-by":"crossref","unstructured":"M.  Taylor,\nVariations on the Donoho\u2013Stark uncertainty principle estimate,\nJ. Geom. Anal. 28 (2018), no. 1, 492\u2013509.","DOI":"10.1007\/s12220-017-9830-3"}],"container-title":["Forum Mathematicum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/forum-2023-0244\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/forum-2023-0244\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T21:21:05Z","timestamp":1724361665000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/forum-2023-0244\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,2]]},"references-count":24,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,12,15]]},"published-print":{"date-parts":[[2024,9,1]]}},"alternative-id":["10.1515\/forum-2023-0244"],"URL":"https:\/\/doi.org\/10.1515\/forum-2023-0244","relation":{},"ISSN":["0933-7741","1435-5337"],"issn-type":[{"value":"0933-7741","type":"print"},{"value":"1435-5337","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,2]]}}}