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We establish the linear independence of time–frequency translates for functions  f  having one‐sided decay lim   x →∞  | f ( x )|  e   cx  log  x  =0 for all  c >0. We also prove such results for functions with faster than exponential decay, that is, lim   x →∞  | f ( x )|  e   cx  =0 for all  c >0, under some additional restrictions.

Linear independence of time–frequency translates of functions with faster than exponential decay