Twisted sheaves on complex spaces
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.
We prove that every Kähler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algebraic groups in the case where the isotropy has the property that its intersection with the radical is Zariski dense in the radical.
It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with -smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely connected planar domain.
We give some explicit values of the constants and in the inequality where denotes the norm of the Bergman projection on the space.