White noise space analysis and multiplicative change of measures

Daniel Alpay, Palle Jorgensen, Motke Porat

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number042102
JournalJournal of Mathematical Physics
Issue number4
StatePublished - 1 Apr 2022

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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