37 citations · 144 across the 42 of their papers we have counts for
51 papers
Isomorphic Busemann--Petty for arbitrary measures: the sharp order
Alexander Koldobsky, Artem Zvavitch
Let be the optimal constant with the following property. For every even, continuous, strictly positive density on and all origin-symmetric convex bodies $K,L\subset…
Functions positively associated with integral transforms
Alexander Koldobsky
We introduce the class of functions positively associated with a linear operator. We describe these classes for several integral operators including the -cosine transform and th…
Radon transforms with small derivatives and distance inequalities for convex bodies
Julián Haddad, Alexander Koldobsky
Generalizing the slicing inequality for functions on convex bodies from [11], it was proved in [4] that there exists an absolute constant so that for any , any…
Comparison Problems for Radon Transforms
Alexander Koldobsky, Michael Roysdon, Artem Zvavitch
Given two non-negative functions and such that the Radon transform of is pointwise smaller than the Radon transform of , does it follow that the -norm of is…
Inequalities for sections and projections of convex bodies
Apostolos Giannopoulos, Alexander Koldobsky, Artem Zvavitch
This article belongs to the area of geometric tomography, which is the study of geometric properties of solids based on data about their sections and projections. We describe a new…
Algebraically integrable bodies and related properties of the Radon transform
Mark Agranovsky, Jan Boman, Alexander Koldobsky +2
Generalizing Lemma 28 from Newton's ``Principia", Arnold asked for a complete characterization of algebraically integrable domains. In this paper we describe the current state of A…