UNIQUENESS FOR THE NONHARMONIC FOURIER SERIES OF DISTRIBUTIONS

We generalize the uniqueness theorem of K.Yoneda[9] for nonharmonic series under a much weaker condition as follows: Let ｛λ$_{k}$ ｝$_{k}$ =$o^{\infty}$ be a discrete sequence in $R^n$. If (equation omitted) = 0 for all x $\in$ $R^n$ and there exists a number N > 0 such that (equation omitted) then$ a_{k}$ = 0 for all k $\in$ $N_{0}$.