A note on the $M^*$–limiting convolution body
Antonis Tsolomitis
We introduce the mixed convolution bodies of two convex symmetric bodies. We prove that if the boundary of a body $K$ is smooth enough then as $\delta$ tends to $1$ the $\delta$–$M^*$–convolution body of $K$ with itself tends to a multiple of the Euclidean ball after proper normalization. On the other hand we show that the $\delta$–$M^*$–convolution body of the $n$–dimensional cube is homothetic to the unit ball of $\ell_1^n$.