Abel-Tauber theorems for Fourier-Stieltjes coefficients

[摘要] We prove Abel-Tauber theorems which link the asymptotics of a function and its Fourier-Stieltjes coefficients under a weak Tauberian condition. Both cosine and sine coefficients are studied. The results in the cosine case can be applied to stationary time series with long-time memory. The analogues for Fourier-Stieltjes transforms are also given. (C) 1997 Academic Press.

[发布日期] 1997-07-15