  We prove new kinematic formulas for tensor valuations and simplify previously
known Crofton formulas by using the recently developed algebraic theory of
translation invariant valuations. The heart of the paper is the computation of
the Alesker-Fourier transform on the large class of spherical valuations, which
is achieved by differential-geometric and representation theoretical tools. We
also describe in explicit form the product and convolution of tensor
valuations.

Differential Geometry;Metric Geometry