Question: For each ((omega, ho)), deduce that the matrix-valued function [ M_{v}left(left|x-x^{prime}ight|ight)left(cos left(omega^{prime}left(x-x^{prime}ight)ight) I_{3}-sin left(omega^{prime}left(x-x^{prime}ight)ight) chi(ho)ight) ] is the covariance function for a stationary Gaussian process

For each $(\omega, ho)$, deduce that the matrix-valued function

\[
M_{v}\left(\left\|x-x^{\prime}ight\|ight)\left(\cos \left(\omega^{\prime}\left(x-x^{\prime}ight)ight) I_{3}-\sin \left(\omega^{\prime}\left(x-x^{\prime}ight)ight) \chi(ho)ight)
\]

is the covariance function for a stationary Gaussian process $Z: \mathbb{R}^{3} ightarrow \mathbb{R}^{3}$.

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