The Reverse Isoperimetric Problem for Gaussian Measure.
Let be the class of all continuous functions on the annulus in with twisted spherical mean whenever and satisfy the condition that the sphere and ball In this paper, we give a characterization for functions in in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in which improve some of the earlier results.
It is known that a local equatorial characterization of zonoids does not exist. The question arises: Is there a subclass of zonoids admitting a local equatorial characterization. In this article a sufficient condition is found for a centrally symmetric convex body to be a zonoid. The condition has a local equatorial description. Using the condition one can define a subclass of zonoids admitting a local equatorial characterization. It is also proved that a convex body whose boundary is an ellipsoid...