Image of the spectral measure of a Jacobi field and the corresponding operators

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dc.creatorBerezansky, Yurij M.
dc.creatorLytvynov, Eugene W.
dc.creatorPulemyotov, Artem D.
dc.date2006-08-14
dc.date.accessioned2026-07-07T07:21:44Z
dc.date.available2026-07-07T07:21:44Z
dc.descriptionBy definition, a Jacobi field $J=(J(ϕ))_{ϕ\in H_+}$ is a family of commuting selfadjoint three-diagonal operators in the Fock space $\mathcal F(H)$. The operators $J(ϕ)$ are indexed by the vectors of a real Hilbert space $H_+$. The spectral measure $ρ$ of the field $J$ is defined on the space $H_-$ of functionals over $H_+$. The image of the measure $ρ$ under a mapping $K^+:T_-\to H_-$ is a probability measure $ρ_K$ on $T_-$. We obtain a family $J_K$ of operators whose spectral measure is equal to $ρ_K$. We also obtain the chaotic decomposition for the space $L^2(T_-,dρ_K)$.
dc.identifierhttps://arxiv.org/abs/math/0608335
dc.identifierhttp://arxiv.org/abs/math/0608335
dc.identifierIntegral Equations Operator Theory 53 (2005), 191--208
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115408
dc.subjectProbability
dc.subjectFunctional Analysis
dc.subject60G20, 60H40, 47B36, 60G51
dc.titleImage of the spectral measure of a Jacobi field and the corresponding operators
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