  Restricted numerical shadow $P^X_A(z)$ of an operator $A$ of order $N$ is a
probability distribution supported on the numerical range $W_X(A)$ restricted
to a certain subset $X$ of the set of all pure states - normalized,
one-dimensional vectors in ${\mathbb C}^N$. Its value at point $z \in {\mathbb
C}$ equals to the probability that the inner product $< u |A| u >$ is equal to
$z$, where $u$ stands for a random complex vector from the set $X$ distributed
according to the natural measure on this set, induced by the unitarily
invariant Fubini-Study measure. For a Hermitian operator $A$ of order $N$ we
derive an explicit formula for its shadow restricted to real states,
$P^{\mathbb R}_A(x)$, show relation of this density to the Dirichlet
distribution and demonstrate that it forms a generalization of the $B$-spline.
Furthermore, for operators acting on a space with tensor product structure,
${\cal H}_A \otimes {\cal H}_B$, we analyze the shadow restricted to the set of
maximally entangled states and derive distributions for operators of order N=4.
