{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:41:06Z","timestamp":1760143266893,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T00:00:00Z","timestamp":1706313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The properties of the unique nontrivial analytic solution, defined implicitly by a functional equation, are pointed out. This work provides local estimations and global inequalities for the involved solution. The corresponding operatorial equation is studied as well. The second part of the paper is devoted to the full classical moment problem, which is an inverse problem. Two constraints are imposed on the solution. One of them requires the solution to be dominated by a concrete convex operator defined on the positive cone of the domain space. A one-dimensional operator is valued, and a multidimensional scalar moment problem is solved. In both cases, the existence and the uniqueness of the solution are proved. The general idea of the paper is to provide detailed information on solutions which are not expressible in terms of elementary functions.<\/jats:p>","DOI":"10.3390\/sym16020152","type":"journal-article","created":{"date-parts":[[2024,1,29]],"date-time":"2024-01-29T04:57:07Z","timestamp":1706504227000},"page":"152","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Functional and Operatorial Equations Defined Implicitly and Moment Problems"],"prefix":"10.3390","volume":"16","author":[{"given":"Octav","family":"Olteanu","sequence":"first","affiliation":[{"name":"Department of Mathematics-Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Choudary, A.D.R., and Niculescu, C.P. (2014). 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Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/S0893-9659(03)00030-2","article-title":"Maximum entropy solutions and moment problem in unbounded domains","volume":"16","author":"Tagliani","year":"2003","journal-title":"Appl. Math. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Inverardi, P.L.N., and Tagliani, A. (2021). Stieltjies and Hamburger reduced moment problem when MaxEnt solution does not exist. Mathematics, 9.","DOI":"10.3390\/math9040309"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s11785-023-01339-7","article-title":"Stability in Truncated Trigonometric Scalar Moment Problems","volume":"17","year":"2023","journal-title":"Complex Anal. Oper. Theory"},{"key":"ref_17","first-page":"111","article-title":"Laguerre-based Hermite-Bernoulli polynomials associated to bilateral series","volume":"11","author":"Khan","year":"2018","journal-title":"Tbil. Math. 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