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arXiv · 2107.10416

Spectral Integrals of Bernoulli Generalized Functionals

Jing Zhang·Caishi Wang·Lu Zhang·Lixia Zhang
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Abstract

Let $\mathcal{S}\subset \mathcal{L}^2 \subset \mathcal{S}^*$ be the Gel'fand triple over the Bernoulli space, where elements of $\mathcal{S}^*$ are called Bernoulli generalized functionals. In this paper, we define integrals of Bernoulli generalized functionals with respect to a spectral measure (projection operator-valued measure) in the framework of $\mathcal{S}\subset \mathcal{L}^2 \subset \mathcal{S}^*$, and examine their fundamental properties. New notions are introduced, several results are obtained and examples are also shown.

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BibTeXRIS

Jing Zhang, Caishi Wang, Lu Zhang, Lixia Zhang. 2021-07-22. Spectral Integrals of Bernoulli Generalized Functionals. https://doi.org/10.1080/17442508.2021.1959586

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