The Radon transform from the cohomological point of view. (English) Zbl 0823.44006

Gindikin, Simon

Gindikin, Simon (ed.) et al., 75 years of Radon transform. Proceedings of the conference held at the Erwin Schrödinger International Institute for Mathematical Physics in Vienna, Austria, August 31-September 4, 1992. Cambridge, MA: International Press. Conf. Proc. Lect. Notes Math. Phys. 4, 123-128 (1994).

Summary: We consider here a connection between Radon transform and \(\overline \partial\)-cohomology. There is an essential connection between hyperfunctions and the Radon transform and its generalization – the Radon-John transform (integration over \(k\)-dimensional planes in \(\mathbb{R}^ n\), \(k < n - 1\)).
For the entire collection see [Zbl 0814.00012].

MSC:

44A12	Radon transform
32C35	Analytic sheaves and cohomology groups
46F15	Hyperfunctions, analytic functionals
32V40	Real submanifolds in complex manifolds
46F20	Distributions and ultradistributions as boundary values of analytic functions

Keywords:

cohomology; Radon transform; hyperfunctions; Radon-John transform