A non-commutative Sobolev estimate and its application to spectral synthesis

In [M. K. Vemuri, Realizations of the canonical representation, Proc. Indian Acad. Sci. Math. Sci., 118 (2008), 115 –131], 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, it is shown that discrete sets are sets of spectral synthesis for the Alpha transform.