Some Extremal Problems for the Fourier Transform on the Hyperboloid

We give the solution of the Turán, Fejér, Delsarte, Logan, and Bohman extremal problems for the Fourier transform on the hyperboloid $\mathbb{H}^{d}$ or Lobachevsky space. We apply the averaging function method over the sphere and the solution of these problems for the Jacobi transform on the half-line.