{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:36:42Z","timestamp":1753886202148,"version":"3.41.2"},"reference-count":18,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,9,5]],"date-time":"2011-09-05T00:00:00Z","timestamp":1315180800000},"content-version":"vor","delay-in-days":247,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"MIM","award":["p83-118"],"award-info":[{"award-number":["p83-118"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>The relation between representations and positive definite functions\nis a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier and Fourier\u2010Stieltjes algebras of an inverse semigroup and study their relation with the corresponding algebras on the associated groupoid.<\/jats:p>","DOI":"10.1155\/2011\/324821","type":"journal-article","created":{"date-parts":[[2011,9,5]],"date-time":"2011-09-05T19:01:00Z","timestamp":1315249260000},"update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Restricted Algebras on Inverse Semigroups\u2014Part II: Positive Definite Functions"],"prefix":"10.1155","volume":"2011","author":[{"given":"Massoud","family":"Amini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alireza","family":"Medghalchi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,9,5]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200410451"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1142\/3645"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012\u20107094\u201071\u201003893\u20102"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02315973"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00233\u2010002\u20100031\u20103"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/1990636"},{"key":"e_1_2_6_7_2","series-title":"London Mathematical Society Monographs","volume-title":"C\u2217-Algebras and Their Automorphism Groups","author":"Pedersen G. 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