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

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