Image of a Jacobi Field.

Consider the two Hilbert spaces H− and T−. Let K+: H− → T- be a bounded operator. Consider a measure ρ on 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 present a family of operators whose spectral measure equals ρK. We state an analogue of the Wiener-Itô decomposition for ρK. Finally, we illustrate our constructions by offering a few examples and exploring a relatively transparent special case. [ABSTRACT FROM AUTHOR]