A new proof of the support theorem and the range characterization for the Radon transform

The aim of this note is to give a new and elementary proof of the support theorem for the Radon transform, which is based only on the projection theorem and the Paley-Wiener theorem for the Fourier transform. The idea is to solve a certain system of linear equations in order to determine the coefficients of a homogeneous polynomial (interpolation problem). By the same method, we get a short proof of the range characterization for Radon transforms of functions supported in a ball.

Beitrag zum Divisionsproblem for Ultradistributionen und ein Fortsetzungssatz

In this note we give a characterization of ultradistributions, which are supported by a single point. As a consequence we get a necessary condition for the solvability of the division problem for ultradistributions similar to the well-known condition in the case of distributions (cf. Malgrange [12]). Finally an extension theorem for ultradistributions is proved, using exponential growth conditions, that generalize the condition of Lojasiewicz [11].

Extension of analytic functional calculus mappings and duality by $$\bar \partial $$ -Closed forms with growth

Holomorphic approximation of ultradifferentiable functions

Introduct ion Let S be a closed subset of some open set in Cn and denote by dT(S) the space of germs of holomorphic functions on (a neighborhood of) S. For a space F(S) of tEvalued (continuous, differentiable etc.) functions on S [containing t~(S)] the problem of holomorphic approximation consists of finding conditions to ensure that the natural mapping Q : e)(S)-~F(S) has dense range with respect to a given topology on F(S). Positive solutions for F = C r, 0_ l . For Q:tP(/3)~O(D)c~C(/3), DCIE n strongly pseudoconvex, proofs were given independently by Henkin [17], Kerzman [21], and Lieb [27], for the case e : (9(/3)~(9(D)c~C~(/3) cf. also [30] and for Sobolev spaces see Bell [3, Sect. 6].…