Image of the Spectral Measure of a Jacobi Field and the Corresponding Operators |
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Authors: | Yurij M. Berezansky Eugene W. Lytvynov Artem D. Pulemyotov |
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Affiliation: | (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 |
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Abstract: | By definition, a Jacobi field is a family of commuting selfadjoint three-diagonal operators in the Fock space 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 is a probability measure ρK on T−. We obtain a family JK of operators whose spectral measure is equal to ρK. We also obtain the chaotic decomposition for the space L2(T−, dρ K). |
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Keywords: | Primary 60G20 60H40 47B36 Secondary 60G51 |
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