On the theory of Radon transformations of hyperfunctions. (English) Zbl 0576.32008

Kataoka, Kiyômi

J. Fac. Sci., Univ. Tokyo, Sect. I A 28, 331-413 (1981).

In this paper several operations on hyperfunctions are explicitly defined using Radon transforms. [On a modern statement of Radon transform see S. Helgason, The Radon transform. (1980; Zbl 0453.43011).] The statement contains details and combines Fourier analysis with the theory of microfunctions. As a result, the author proved in § 2 the coherency of the notion of singular spectrum independently of J. M. Bony. He also proved the independence of support and singular support independently of Kashiwara’s proof.

Reviewer: M.Marinov

MSC:

32A45	Hyperfunctions
46F15	Hyperfunctions, analytic functionals
32A07	Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)

Keywords:

convex tube domain; Radon transformation of hyperfunctions; Radon; transformation of holomorphic microfunctions; holomorphic micro; local operators

Citations:

Zbl 0453.43011