A non-commutative Sobolev estimate and its application to spectral   synthesis
  In [M. K. Vemuri, Realizations of the canonical representation], it was shown that the spectral synthesis problem for the Alpha transform is closely related to the problem of classifying realizations of the canonical representation (of the Heisenberg group). In this paper, we show that discrete sets are sets of spectral synthesis for the Alpha transform. 
M. K. Vemuri