A NOTE ON THE M^{∗}–LIMITING CONVOLUTION BODY

ANTONIS TSOLOMITIS

Abstract. 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 δ tends to 1 the δ–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 δ–M^{∗}–convolution body of the n–dimensional cube is homothetic to the unit ball of ℓ_{1}^{n}.