{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T16:47:35Z","timestamp":1762015655386,"version":"3.41.2"},"reference-count":36,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, Portugal","award":["UIDB\/MAT\/04674\/2020"],"award-info":[{"award-number":["UIDB\/MAT\/04674\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Infin. Dimens. Anal. Quantum. Probab. Relat. Top."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:p> In this paper, we use a biorthogonal approach to the analysis of the infinite dimensional fractional Poisson measure [Formula: see text], [Formula: see text], on the dual of Schwartz test function space [Formula: see text]. The Hilbert space [Formula: see text] of complex-valued functions is described in terms of a system of generalized Appell polynomials [Formula: see text] associated to the measure [Formula: see text]. The kernels [Formula: see text], [Formula: see text], of the monomials may be expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions. Associated to the system [Formula: see text], there is a generalized dual Appell system [Formula: see text] that is biorthogonal to [Formula: see text]. The test and generalized function spaces associated to the measure [Formula: see text] are completely characterized using an integral transform as entire functions. <\/jats:p>","DOI":"10.1142\/s0219025723500157","type":"journal-article","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T16:09:11Z","timestamp":1690560551000},"source":"Crossref","is-referenced-by-count":2,"title":["A biorthogonal approach to the infinite dimensional fractional Poisson measure"],"prefix":"10.1142","volume":"26","author":[{"given":"Jerome B.","family":"Bendong","sequence":"first","affiliation":[{"name":"DMS, MSU-Iligan Institute of Technology, Tibanga, 9200 Iligan City, Philippines"}]},{"given":"Sheila M.","family":"Menchavez","sequence":"additional","affiliation":[{"name":"DMS, MSU-Iligan Institute of Technology, Tibanga, 9200 Iligan City, Philippines"}]},{"given":"Jos\u00e9 Lu\u00eds","family":"da Silva","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias Exatas e da Engenharia, CIMA, Universidade da Madeira, Campus Universit\u00e1rio da Penteada, 9020-105 Funchal, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2023,8,29]]},"reference":[{"key":"S0219025723500157BIB001","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.0067"},{"key":"S0219025723500157BIB002","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1997.3183"},{"key":"S0219025723500157BIB003","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1997.3215"},{"key":"S0219025723500157BIB004","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v14-675"},{"key":"S0219025723500157BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-0509-5"},{"key":"S0219025723500157BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-9185-1"},{"key":"S0219025723500157BIB008","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1409932670"},{"key":"S0219025723500157BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6956-8"},{"key":"S0219025723500157BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2019.03.006"},{"key":"S0219025723500157BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2021.109285"},{"volume-title":"Generalized Functions","year":"1968","author":"Gel\u2019fand I. 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