On Links Between a Theorem of Schoenberg, Rohlin Decompositions of Measures, the Bochner-Minlos Theorem and the Fock Space

Authors

• Daniel Alpay, Chapman UniversityFollow
• Paula Cerejeiras, University of Aveiro
• Palle Jorgensen, University of Iowa
• Uwe Kaehler, University of Aveiro

Document Type

Article

Publication Date

3-31-2026

Abstract

The main goal of this paper is to gain new results in stochastics by drawing on, and combining, different areas that are normally not considered to be related. Thus, in this paper we extend the previous class of Gaussian-like functions ML which will allow for future generalized stochastic processes in infinite dimensional analysis. We show that an approach similar to the one by the classical Bochner-Minlos theorem for the white-noise case can be achieved by using Gaussian-like functions belonging to a large family -the ML_r classes (0 < r ≤∞). We show how Schoenberg’s theorem for positive definite functions on a Hilbert space allows to go beyond the classical setting of Bochner-Milnos theorem. Furthermore, we show that the application of the Rohlin’s disintegration theorem allows for a decomposition of the associated probability measures , see Theorems 3.2 and 4.3. We end this paper with several important examples of functions in these classes ML_r and provide some interesting counterexamples, e.g. Theorem 7.4, to get a better feeling on this classes.

Comments

This article was originally published in Analysis and Mathematical Physics, volume 16, in 2026. https://doi.org/10.1007/s13324-026-01190-x

Recommended Citation

Alpay, D., Cerejeiras, P., Jorgensen, P. et al. On links between a theorem of Schoenberg, Rohlin decompositions of measures, the Bochner-Minlos theorem and the Fock space. Anal. Math. Phys. 16, 45 (2026). https://doi.org/10.1007/s13324-026-01190-x

Peer Reviewed

1

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.