Fourier transforms in spaces of hyperfunctions and Hartogs’ type phenomena. (English) Zbl 1030.46053
Chen, Hua (ed.) et al., Partial differential equations and their applications. Proceedings of the conference, Wuhan, China, April 5-9, 1999. Singapore: World Scientific. 152-166 (1999).
This paper reports on some applications of the theory of the local Fourier transform for hyperfunctions and the related duality theory for the space \(B/A\), where \(B\) is the space of germs of hyperfunctions at \(0 \in \mathbb{R}^{n}\) and \(A\) is the subspace of real-analytic functions in \(B\). Some results on the existence of boundary traces for one-sided solutions of linear partial pseudodifferential equations in the \(C^{\infty}\) case and the analytic case are given. Then, Hartogs type phenomena for hyperfunctions with holomorphic parameters are described. The proofs of these results are not given here.
For the entire collection see [Zbl 0969.00056].
For the entire collection see [Zbl 0969.00056].
Reviewer: Na Jisheng (Beijing)
MSC:
46F15 | Hyperfunctions, analytic functionals |
35A27 | Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs |
32S05 | Local complex singularities |
46F20 | Distributions and ultradistributions as boundary values of analytic functions |