EXPERIMENTAL APPROACHES TO KUTTNER’S PROBLEM

TILMANN GNEITING, KJELL KONIS, AND DONALD RICHARDS

Abstract. For λ ∈ (0, 2), let k(λ) denote the smallest positive value of κ so that the truncated power function φ_{λ,κ}(t) = (1−|t|^{λ})_{+}^{κ} is positive definite. We give lower and upper estimates of Kuttner’s function k(λ) through detailed numerical and symbolic computations, and we show analytically that k(\frac{4n+1}{2n+1}) ≤ 2n+1 for n ∈ ℕ.