The Penrose transform is discussed for the Dirac equation corresponding to an orthogonal group in even dimensions. The authors outline a simple approach to the calculation which involves using the Dolbeault realization of cohomology groups rather than hypercohomology and spectral sequence. The details will be given elsewhere.
The author uses the concept of the first principal prolongation of an arbitrary principal filter bundle to develop an alternative procedure for constructing the prolongations of a class of the first-order -structures. The motivation comes from the almost Hermitian structures, which can be defined either as standard first-order structures, or higher-order structures, but if they do not admit a torsion-free connection, the classical constructions fail in general.
[For the entire collection see Zbl 0742.00067.]Let be the set of hyperplanes in , the unit sphere of , the exterior of the unit ball, the set of hyperplanes not passing through the unit ball, the Radon transform, its dual. as operator from to is a closable, densely defined operator, denotes the operator given by if the integral exists for a.e. Then the closure of is the adjoint of . The author shows that the Radon transform and its dual can be linked by two operators...