For an inner function θ on the upper half-plane ℂ+, we look at the star-invariant subspace ${\mathrm{K}}_{0}^{\mathrm{p}}:={\mathrm{H}}^{\mathrm{p}}\cap \mathrm ...

Let Fn be a free group of rank n with free basis x1, ⋯, xn. Let {y1, ⋯, yk} be a set of k ≤ n elements of Fn, where each yi is represented by a word Yi(x1, ⋯, xn) in the generators xj. Let ∂ yi/∂ xj ...