Lubin-Tate generalizations of the p-adic Fourier transform

Fresnel and de Mathan proved that the p-adic Fourier transform is surjective. We reinterpret their result in terms of analytic boundaries, and extend it beyond the cyclotomic case. We also give some applications of their result to Schneider and Teitelbaum's p-adic Fourier theory, in particular to generalized Mahler expansions and to the geometry of the character variety.