Moscow--Petersburg seminar on low-dimensional mathematics
SPb, PDMI, 15.03.2002, 16:00--17:45, room 311

G.Litvinov.
Integral Geometry and hypergroups.

It is well known that the Radon Transform is closely related to the Fourier
transform and harmonic analysis on the group of real numbers (or the
additive groups of vectors in a finite dimensional real linear space).
Similarly there are relations between some standard problems of Integral
Geometry (in the sense of Gelfand and Graev) and some commutative
hypergroups (in the sense of J. Delsarte) and harmonic analysis on these
hypergoups. This result can be treated as an answer for an old 
I.M.Gelfand's question on algebraic foundations of Integral Geometry.

The talk is based on joint results of the speaker with M.I.Graev.