{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T16:23:42Z","timestamp":1762273422299,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,13]],"date-time":"2025-04-13T00:00:00Z","timestamp":1744502400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper establishes explicit inversion formulae for the Widder\u2013Lambert transform and the Stieltjes\u2013Poisson transform, extending their applicability to function spaces and compactly supported distributions. Utilizing a generalized Lambert transform, the study provides a unified framework for inversion, enhancing the theoretical understanding of these integral transforms. Additionally, a specific function class satisfying Salem\u2019s equivalence to the Riemann hypothesis is identified, further broadening the analytical scope of the results within generalized function spaces.<\/jats:p>","DOI":"10.3390\/axioms14040291","type":"journal-article","created":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T04:42:07Z","timestamp":1744605727000},"page":"291","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New Inversion Formulae for the Widder\u2013Lambert and Stieltjes\u2013Poisson Transforms"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5506-5050","authenticated-orcid":false,"given":"Emilio R.","family":"Negr\u00edn","sequence":"first","affiliation":[{"name":"Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna (ULL), ES-38271 La Laguna, Spain"},{"name":"Instituto de Matem\u00e1ticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), ULL Campus de Anchieta, ES-38271 La Laguna, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6569-8540","authenticated-orcid":false,"given":"Jeetendrasingh","family":"Maan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Scientific Computing, National Institute of Technology, Hamirpur 177005, India"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.2307\/3029825","article-title":"An inversion of the Lambert transform","volume":"23","author":"Widder","year":"1950","journal-title":"Math. 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