Spectral theory and Wiener-Itô decomposition for the image of a Jacobi field
Assume that K⁺ : H_ → T_ is a bounded operator, where H_ and T_ are Hilbert spaces and ρ is a measure on the space H_. Denote by ρK the image of the measure ρ under K⁺. This paper aims to study the measure ρK assuming ρ to be the spectral measure of a Jacobi field. We obtain a family of operators...
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| Date: | 2007 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2007
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/164192 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Spectral theory and Wiener-Itô decomposition for the image of a Jacobi field / Yu.M. Berezansky, A.D. Pulemyotov // Український математичний журнал. — 2007. — Т. 59, № 6. — С. 744–763. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Assume that K⁺ : H_ → T_ is a bounded operator, where H_ and T_ are Hilbert spaces and ρ is a measure
on the space H_. Denote by ρK the image of the measure ρ under K⁺. This paper aims to study the measure
ρK assuming ρ to be the spectral measure of a Jacobi field. We obtain a family of operators whose spectral
measure equals ρK. We also obtain an analogue of the Wiener – Ito decomposition for ˆ ρK. Finally, we illustrate
the results obtained by carrying out the explicit calculations for the case, where ρK is a Levy noise measure. |
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