On a class of shift-invariant subspaces of the Drury-Arveson space

In the Drury-Arveson space, we consider the subspace of functions whose Taylor coefficients are supported in a set Y subset of N-d with the property that N\X + e(j) subset of N\X for all j = 1,..., d. This is an easy example of shift-invariant subspace, which can be considered as a RKHS in is own right, with a kernel that can be explicitly calculated for specific choices of X. Every such a space can be seen as an intersection of kernels of Hankel operators with explicit symbols. Finally, this is the right space on which Drury's inequality can be optimally adapted to a sub-family of the commuting and contractive operators originally considered by Drury.