{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:50:34Z","timestamp":1760057434705,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T00:00:00Z","timestamp":1739145600000},"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 presents a comprehensive study of Plancherel\u2019s theorem and inversion formulae for the Widder\u2013Lambert transform, extending its scope to Lebesgue integrable functions, compactly supported distributions, and regular distributions with compact support. By employing the Plancherel theorem for the classical Mellin transform, we derive a corresponding Plancherel\u2019s theorem specific to the Widder\u2013Lambert transform. This novel approach highlights an intriguing connection between these integral transforms, offering new insights into their role in harmonic analysis. Additionally, we explore a class of functions that satisfy Salem\u2019s equivalence to the Riemann hypothesis, providing a deeper understanding of the interplay between such equivalences and integral transforms. These findings open new avenues for further research on the Riemann hypothesis within the framework of integral transforms.<\/jats:p>","DOI":"10.3390\/axioms14020129","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T05:53:22Z","timestamp":1739166802000},"page":"129","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Mellin and Widder\u2013Lambert Transforms with Applications in the Salem Equivalence to the Riemann Hypothesis"],"prefix":"10.3390","volume":"14","author":[{"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, Tenerife, Spain"},{"name":"Instituto de Matem\u00e1ticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), ULL Campus de Anchieta, ES-38271 La Laguna, Tenerife, 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"}]},{"given":"Benito J.","family":"Gonz\u00e1lez","sequence":"additional","affiliation":[{"name":"Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna (ULL), ES-38271 La Laguna, Tenerife, Spain"},{"name":"Instituto de Matem\u00e1ticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), ULL Campus de Anchieta, ES-38271 La Laguna, Tenerife, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,10]]},"reference":[{"key":"ref_1","unstructured":"Zayed, A.I. 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