Journal article
White Noise Space Analysis and Multiplicative Change of Measures
Journal of mathematical physics, Vol.63(4), 042102
04/01/2022
DOI: 10.1063/5.0042756
Abstract
In this paper, we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a corresponding family of representations of the canonical commutation relations (CCR) in an infinite number of degrees of freedom. A key feature of our construction is explicit formulas for associated transforms; these are infinite-dimensional analogs of Fourier transforms. Our framework is that of Gaussian Hilbert spaces, reproducing kernel Hilbert spaces and Fock spaces. The latter forms the setting for our CCR representations. We further show, with the use of representation theory and infinite-dimensional analysis, that our pairwise inequivalent probability spaces (for the Gaussian processes) correspond in an explicit manner to pairwise disjoint CCR representations.
Details
- Title: Subtitle
- White Noise Space Analysis and Multiplicative Change of Measures
- Creators
- Daniel Alpay - Chapman UniversityPalle JorgensenMotke Porat - Ben-Gurion University of the Negev
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical physics, Vol.63(4), 042102
- DOI
- 10.1063/5.0042756
- ISSN
- 0022-2488
- eISSN
- 1089-7658
- Publisher
- AIP Publishing
- Grant note
- DOI: 10.13039/501100001742, name: United States-Israel Binational Science Foundation, award: 2010432; DOI: 10.13039/501100001659, name: Deutsche Forschungsgemeinschaft, award: SCHW 1723/1-1; DOI: 10.13039/501100003977, name: Israel Science Foundation, award: 2123/17
- Language
- English
- Date published
- 04/01/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984531959802771
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