Abstract
The relative Dolbeault cohomology which naturally comes up in the theory of Čech–Dolbeault cohomology turns out to be canonically isomorphic with the local (relative) cohomology of Grothendieck and Sato so that it provides a handy way of representing the latter. In this paper we use this cohomology to give simple explicit expressions of Sato hyperfunctions, some fundamental operations on them and related local duality theorems. This approach also yields a new insight into the theory of hyperfunctions and leads to a number of further results and applications. As one of such, we give an explicit embedding morphism of Schwartz distributions into the space of hyperfunctions.
Funding Statement
The first named author was supported by JSPS Grants 18K03316 and 21K03284. The third named author was supported by JSPS Grants 16K05116 and 20K03572.
Citation
Naofumi HONDA. Takeshi IZAWA. Tatsuo SUWA. "Sato hyperfunctions via relative Dolbeault cohomology." J. Math. Soc. Japan 75 (1) 229 - 290, January, 2023. https://doi.org/10.2969/jmsj/87668766
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