The projection spectral theorem and Jacobi fields

TL;DR

This paper reviews how Berezansky's projection spectral theorem applies to Jacobi fields in symmetric Fock spaces, resulting in the development of Levy white noise measures, and highlights the connections between these mathematical concepts.

Contribution

It introduces new applications of the projection spectral theorem to Jacobi fields, expanding the understanding of Levy white noise measures in quantum probability.

Findings

Established links between spectral theorem and Levy white noise measures

Extended the application of spectral theorem to Jacobi fields in Fock space

Provided insights into the structure of quantum stochastic processes

Abstract

We review several applications of Berezansky's projection spectral theorem to Jacobi fields in a symmetric Fock space, which lead to L\'evy white noise measures.