Hebrew University, Jerusalem, Israel
The Cauchy problem for the Euler-Poisson-Darboux equation on the sphere and various transforms of integral geometry (including those of Minkowski and Funk) give rise to a family of fractional integrals associated with a spherical cap of a fixed radius. These fractional integrals are called the generalized Minkowski-Funk transforms. Investigation of injectivity, invertibility and boundedness of these transforms in Sobolev spaces leads to small denominators for spherical harmonic expansions and to some delicate problems related to arithmetical properties of zeros of the associated Legendre functions.
Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.
[ Spring 2000]