On Abel-Tauber theorems for Fourier cosine transforms (Q1910090)

The aim of the paper is to prove Abel-Tauber theorems for Fourier cosine series and integrals which are closely related to results of Pitman and Soni and Soni. The asymptotic behaviour \(f(t)\sim t^{- 1}\) for \(t\to \infty\) is characterized in terms of the Fourier cosine transform of \(f\), where \(f\) is a locally integrable eventually non-increasing function on \([0, \infty)\) with \(\lim_{t\to \infty} f(t)= 0\). Applications to probability distributions and stationary processes are given.