Über ein Turánsches problem für ℓ-1 radiale, positiv definite Funktionen, II

Turán's problem is to determine the greatest possible value of the integral for positive definite functions f(x), x∈Rd, supported in a given convex centrally symmetric body D⊂Rd, d∈N. We consider the problem for positive definite functions of the form f(x)=ϕ(∥x∥1), x∈Rd, with ϕ supported in [0,π], extending results of our first paper from two to arbitrary dimensions.Our two papers were motivated by investigations of Professor Y. Xu and the 2nd named author on, what they called, ℓ-1 summability of the inverse Fourier integral on Rd. Their investigations gave rise to a pair of transformations (hd,md) on R+ which they studied using special functions, in particular spherical Bessel functions.To study the d-dimensional Turán problem, we had to extend relevant results of B. & X., and we did so using again Bessel functions. These extentions seem to us to be equally interesting as the application to Turán's problem.