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Boundary values of cohomology classes as hyperfunctions. (English) Zbl 0884.32007

Summary: The lecture outlines the contents of the article by P. D. Cordaro, S. Gindikin and F. Treves [J. Funct. Anal. 131, No. 1, 183-227 (1995; Zbl 0847.32007)] which purports to formalize in the framework of hyperfunction theory the concept of the boundary value of a cohomology class (with coefficients in the sheaf of germs of holomorphic functions) propounded in works of Gindikin. In the article [loc. cit.] of Cordaro-Gindikin-Treves the hyperfunctions are defined on a maximally real submanifold of a complex space (and more generally on a hypo-analytic manifold). The formalization is facilitated by the treatment of hyperfunctions and of the boundary values of holomorphic functions in the recent monograph by P. D. Cordaro and F. Treves [‘Hyperfunctions on hypo-analytic manifolds’ (1994; Zbl 0817.32001)]. In order to avoid technicalities that would obscure the overall picture, the present lecture deals only with hyperfunctions in Euclidean space \(\mathbb{R}^n\).

MSC:

32A45 Hyperfunctions
46F15 Hyperfunctions, analytic functionals
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