[For the entire collection see Zbl 0742.00067.]The Penrose transform is always based on a diagram of homogeneous spaces. Here the case corresponding to the orthogonal group $SO(2n,C)$ is studied by means of Clifford analysis [see F. Brackx, R. Delanghe and F. Sommen: Clifford analysis (1982; Zbl 0529.30001)], and is presented a simple approach using the Dolbeault realization of the corresponding cohomology groups and a simple calculus with differential forms (the Cauchy integral formula for solutions of...

[For the entire collection see Zbl 0742.00067.]Let $P^m$ be the set of hyperplanes $\sigma :\langle \overrightarrow{x},\overrightarrow{\theta }\rangle =p$ in ${ℛ}^m$, $S^{m-1}$ the unit sphere of ${ℛ}^m$, $E^m$ the exterior of the unit ball, $T^m$ the set of hyperplanes not passing through the unit ball, $Rf(\overrightarrow{\theta },p)={\int }_{\sigma }f\left(\overrightarrow{x}\right)d\overrightarrow{x}$ the Radon transform, $R^{\#}g\left(\overrightarrow{x}\right)={\int }_{S^{m-1}}g(\overrightarrow{\theta },\langle \overrightarrow{x},\overrightarrow{\theta }\rangle )d{S}_{\overrightarrow{\theta }}$ its dual. $R$ as operator from $L^2\left({ℛ}^m\right)$ to $L^2(S^{m-1)}\times ℛ)$ is a closable, densely defined operator, $R^{*}$ denotes the operator given by $\left(R^{*}g\right)\left(\overrightarrow{x}\right)=R^{\#}g\left(\overrightarrow{x}\right)$ if the integral exists for $\overrightarrow{x}\in {ℛ}^m$ a.e. Then the closure of $R^{*}$ is the adjoint of $R$. The author shows that the Radon transform and its dual can be linked by two operators...

[For the entire collection see Zbl 0742.00067.]Differential spaces, whose theory was initiated by R. Sikorski in the sixties, provide an abstract setting for differential geometry. In this paper the author studies the wedge sum of such spaces and deduces some basic results concerning this construction.