Abel–Tauber Theorems for Fourier–Stieltjes Coefficients

✍ Scribed by A Inoue

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 242 KB
• Volume: 211
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5479

✦ Synopsis

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.