Image of the Spectral Measure of a Jacobi Field and the Corresponding Operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Image of the Spectral Measure of a Jacobi Field and the Corresponding Operators

Authors:	Yurij M Berezansky Eugene W Lytvynov Artem D Pulemyotov

Institution:	(1) Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, 01601 Kyiv, Ukraine;(2) Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, United Kingdom;(3) Department of Mathematics and Mechanics, Kyiv National T. Shevchenko University, 64 Volodymyrs’ka, 01033 Kyiv, Ukraine

Abstract:	By definition, a Jacobi field $J = (\tilde J(\phi ))_{\phi \in H_ + }$ 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 L²(T₋, d_{ρ K}).

Keywords:	Primary 60G20 60H40 47B36 Secondary 60G51
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