  The Branson-Gover operators are conformally invariant differential operators
of even degree acting on differential forms. They can be interpolated by a
holomorphic family of conformally invariant integral operators called
fractional Branson-Gover operators. For Euclidean spaces we show that the
fractional Branson-Gover operators can be obtained as Dirichlet-to-Neumann
operators of certain conformally invariant boundary value problems,
generalizing the work of Caffarelli-Silvestre for the fractional Laplacians to
differential forms. The relevant boundary value problems are studied in detail
and we find appropriate Sobolev type spaces in which there exist unique
solutions and obtain the explicit integral kernels of the solution operators as
well as some of its properties.
