 9495 Ramanathan J., Steger T.
 Incompleteness of Sparse Coherent States
(25K, LaTeX)
Apr 18, 94

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We study necessary conditions for a set of phase space translates of
an arbitrary function $f \in L^2({\bf R}^n)$ to be complete, a frame or
a Riesz basis. The necessary conditions are given in terms of the density
of the underlying set of phase space translates. Among our results
is an elementary proof of a theorem of M. Rieffel's that states that the
set of phase space translates of a function is always incomplete if the
underlying set is a lattice of density less than one. We also prove that if
a set of uniformly discrete phase space translates of a square integrable
function forms a Riesz basis, then the asymptotic density must be exactly equal
to one. An improvement of a result of H.J. Landau concerning necessary
density conditions for a set of coherent states to be a frame is also given.
 Files:
9495.tex