Transactions of the American Mathematical Society, Vol. 366, No. 6 (JUNE 2014), pp. 3275-3293 (19 pages) Inversion theorems of Wiener type are essential tools in analysis and number theory. We derive ...

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 ...