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Convolution of convex valuations

Bernig, Andreas ; Fu, Joseph

In: Geometriae Dedicata, 2006, vol. 123, no. 1, p. 153-169

Convolution of convex valuations

Bernig, Andreas ; Fu, Joseph H. G.

In: Geometriae Dedicata, 2006, vol. 123, no. 1, p. 153-169

We show that the natural “convolution” on the space of smooth, even, translation- invariant convex valuations on a euclidean space V, obtained by intertwining the product and the duality transform of S. Alesker J. Differential Geom. 63: 63–95, 2003; Geom.Funct. Anal. 14:1–26, 2004 may be expressed in terms of Minkowski sum. Furthermore the resulting product extends naturally to odd...