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Math."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p> In this paper, we study the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are obtained. To achieve such a goal, the main technique consists in introducing eight new convolutions weighted by multi-dimensional Hermite functions and using them as convolutions somehow associated with our integral equations. In this way, two Young-type inequalities are also obtained. <\/jats:p>","DOI":"10.1142\/s1793557122501510","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T05:25:10Z","timestamp":1633929910000},"source":"Crossref","is-referenced-by-count":5,"title":["Convolutions and integral equations weighted by multi-dimensional Hermite functions"],"prefix":"10.1142","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4261-8699","authenticated-orcid":false,"given":"L. P.","family":"Castro","sequence":"first","affiliation":[{"name":"CIDMA \u2013 Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"R. C.","family":"Guerra","sequence":"additional","affiliation":[{"name":"CMUC \u2013 Center for Mathematics of the University of Coimbra, Department of Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001-501 Coimbra, Portugal"}]},{"given":"N. M.","family":"Tuan","sequence":"additional","affiliation":[{"name":"Dept. of Math., VNU University of Education, Viet Nam National University, 144 Xuan Thuy str., Cau Giay dist., Ha Noi, Vietnam"}]}],"member":"219","published-online":{"date-parts":[[2021,11,13]]},"reference":[{"key":"S1793557122501510BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s11277-016-3567-3"},{"key":"S1793557122501510BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2012.07.041"},{"key":"S1793557122501510BIB003","doi-asserted-by":"publisher","DOI":"10.1080\/10652460412331320395"},{"key":"S1793557122501510BIB004","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200310110"},{"key":"S1793557122501510BIB005","first-page":"7","volume":"66","author":"Castro L. P.","year":"2015","journal-title":"Mem. Differ. Equ. Math. Phys."},{"issue":"1","key":"S1793557122501510BIB006","first-page":"020037","volume":"1798","author":"Castro L. P.","year":"2017","journal-title":"Am. Inst. Phys. Conf. 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