Nonnegative Fourier–Jacobi Coefficients and Some Classes of Functions Original Research Article

Fourier–Jacobi series with nonnegative Fourier–Jacobi coefficients are considered. Under special restrictions on the Jacobi weight function, we establish in terms of Fourier–Jacobi coefficients a necessary and sufficient condition in order that the sum of the Fourier–Jacobi series should possess certain structural properties.