Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score
based on the predictive distribution and on the event or value that materializes. A scoring …

The Wiener algebra of absolutely convergent Fourier integrals: an overview | SpringerLink
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The study of the geometry of convex bodies based on information about sections and
projections of these bodies has important applications in many areas of mathematics and …

We derive a formula connecting the derivatives of parallel section functions of an origin-
symmetric star body in Rn with the Fourier transform of powers of the radial function of the …

Abstract The 1956 Busemann-Petty problem asks whether symmetric convex bodies with
larger central hyperplane sections also have greater volume. In 1988, Lutwak introduced the …

In many scientific disciplines, straight line, Euclidean distances may not accurately describe
proximity relationships among spatial data. However, non-Euclidean distance measures …

Minkowski's Theorem asserts that every centered measure on the sphere which is not
concentrated on a great subsphere is the surface area measure of some convex body, and …

Let ρ be a nonnegative homogeneous function on R n. General structure of the set of
numerical pairs (δ, λ), for which the function (1− ρλ (x)) δ+ is positive definite on R n is …

We express the volume of central hyperplane sections of star bodies in R n in terms of the
Fourier transform of a power of the radial function, and apply this result to confirm the …

This article presents sufficient conditions for the positive definiteness of radial functions $ f
(x)=\varphi (\| x\|) $, $ x\in\mathbb {R}^ n $, in terms of the derivatives of $\varphi $. The …