Nonstandard Proofs of Herglotz, Bochner and Bochner–Minlos Theorems
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Birkhauser Boston
Abstract
We 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.
Description
Keywords
Bochner’s theorem, Nonstandard analysis, Positive-definite functions, Stone-(formula presented.) ech compactification