A RIEMANN-LEBESGUE LEMMA FOR FOURIER-JACOBI COEFFICIENTS - Fejzullahu, Bujar Xh. (Matematichki Bilten, 2006)
Riemann-Lebesgue Lemma for Fourier-Jacobi coefficients for the class of functions in \(L^p_(α,β)\), \(1<p≤∞\), are studied. In [3], it is proved that \[ _k→∞f_(α,β)(k)=0 \] holds for each \(fL^1_(α,β)\) if and only if \(α≥β>-1\), \(α≥-1/2\). For \(fL^p_(α,β)\), \(1<p≤∞\), and \(α>-1/2\), \(β>-1\) Riemann-Lebesgue Lemma is proved.