{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T01:53:31Z","timestamp":1776650011064,"version":"3.51.2"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100010874","name":"Shandong Provincial Finance Department","doi-asserted-by":"publisher","award":["ZR2023QA118"],"award-info":[{"award-number":["ZR2023QA118"]}],"id":[{"id":"10.13039\/501100010874","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p> The Windowed Special Affine Fourier Transform (WSAFT) extends classical windowed Fourier transforms through a parameter matrix, enabling precise signal adaptation and superior time-frequency localization for non-stationary signals. Unlike the special affine Fourier transform with its global kernel, WSAFT captures local frequency components that traditional methods cannot resolve. This work establishes a novel univariate integral reconstruction framework, overcoming computational limitations of conventional double-integration methods. We present that a signal can be reconstructed from its WSAFT with a univariate integral. For continuous window functions [Formula: see text] satisfying [Formula: see text], we prove that the reconstruction integral converges both in [Formula: see text]-norm for all [Formula: see text] and almost everywhere on [Formula: see text]. Through Ces\u00e0ro summability, we extend these results to [Formula: see text] signals, achieving norm convergence for all [Formula: see text] and pointwise almost everywhere convergence. These theoretical findings are validated by representative examples using Gaussian window functions and signals. <\/jats:p>","DOI":"10.1142\/s0219691325500249","type":"journal-article","created":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T06:01:27Z","timestamp":1753509687000},"source":"Crossref","is-referenced-by-count":1,"title":["Inversion formula for the windowed special affine Fourier transform"],"prefix":"10.1142","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4076-1026","authenticated-orcid":false,"given":"Yaoyao","family":"Han","sequence":"first","affiliation":[{"name":"School of Science, Shandong Jianzhu University, 1000 Fengming Road, Jinan 250101, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2025,8,21]]},"reference":[{"key":"S0219691325500249BIB001","doi-asserted-by":"publisher","DOI":"10.1364\/OL.19.001801"},{"key":"S0219691325500249BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1977.10770"},{"key":"S0219691325500249BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2017.07.002"},{"key":"S0219691325500249BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392815"},{"key":"S0219691325500249BIB005","series-title":"Graduate Studies in Mathematics","volume-title":"Fourier Analysis","volume":"29","author":"Duoandikoetxea J.","year":"2001"},{"key":"S0219691325500249BIB006","doi-asserted-by":"publisher","DOI":"10.1002\/mma.9907"},{"key":"S0219691325500249BIB007","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2021.1955860"},{"key":"S0219691325500249BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s00006-022-01228-w"},{"key":"S0219691325500249BIB009","doi-asserted-by":"publisher","DOI":"10.4064\/sm-68-1-79-83"},{"key":"S0219691325500249BIB010","doi-asserted-by":"publisher","DOI":"10.1063\/1.1665805"},{"key":"S0219691325500249BIB011","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/25.3.241"},{"key":"S0219691325500249BIB012","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.20.000522"},{"key":"S0219691325500249BIB013","volume-title":"Real and Complex Analysis","author":"Rudin W.","year":"1987","edition":"3"},{"key":"S0219691325500249BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s11868-019-00319-w"},{"key":"S0219691325500249BIB015","doi-asserted-by":"publisher","DOI":"10.1002\/mana.201000128"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691325500249","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T08:41:54Z","timestamp":1760344914000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691325500249"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,21]]},"references-count":15,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10.1142\/S0219691325500249"],"URL":"https:\/\/doi.org\/10.1142\/s0219691325500249","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,21]]},"article-number":"2550024"}}