Spectral theory and Wiener-Itô decomposition for the image of a Jacobi field - Berezansky, Yu.M.; Pulemyotov, A.D. (Український математичний журнал, 2007)
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.