Nonstandard Proofs of Herglotz, Bochner and Bochner–Minlos Theorems

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dc.contributor.authorTlas, Tamer
dc.contributor.departmentDepartment of Mathematics
dc.contributor.facultyFaculty of Arts and Sciences (FAS)
dc.contributor.institutionAmerican University of Beirut
dc.date.accessioned2025-01-24T11:24:34Z
dc.date.available2025-01-24T11:24:34Z
dc.date.issued2015
dc.description.abstractWe describe a unified approach to Herglotz, Bochner and Bochner–Minlos theorems using a combination of Daniell integral and nonstandard analysis. The proofs suggest a natural extension of the last two theorems to the case when the characteristic function is not continuous. This extension is proven and is demonstrated to be the best one possible. © 2014, Springer Science+Business Media New York.
dc.identifier.doihttps://doi.org/10.1007/s00041-014-9368-8
dc.identifier.eid2-s2.0-84943589264
dc.identifier.urihttp://hdl.handle.net/10938/26024
dc.language.isoen
dc.publisherBirkhauser Boston
dc.relation.ispartofJournal of Fourier Analysis and Applications
dc.sourceScopus
dc.subjectBochner’s theorem
dc.subjectNonstandard analysis
dc.subjectPositive-definite functions
dc.subjectStone-(formula presented.) ech compactification
dc.titleNonstandard Proofs of Herglotz, Bochner and Bochner–Minlos Theorems
dc.typeArticle

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