On Ball Numbers

Abstract

We first shortly review, in part throwing a new light on, basics of ball numbers for balls having a positively homogeneous Minkowski functional and turn over then to a new particular class of ball numbers of balls having a Minkowski functional being homogeneous with respect to multiplication with a specific diagonal matrix. Applications to crystal breeding, temperature expansion and normalizing density generating functions in big data analysis are indicated and a challenging problem from the inhomogeneity program is stated.

Keywords

• norm and antinorm ball
• matrix homogeneous ball
• star body
• star radius
• norm and antinorm radius
• <i>p</i>-spherical radius parameter
• dual surface content measure
• density normalizing constant
• crystal breeding
• temperature expansion