Embedding of infinitely differentiable functions into the space of hyperfunctions via Čech–Dolbeault cohomology and its inverse map
Tatsuki NISHIDA · Journal of the Mathematical Society of Japan · 2025
Honda, Izawa and Suwa define Čech–Dolbeault representation of hyperfunctions and an embedding of distributions to the space of hyperfunctions. With this embedding, we can regard $C^{\infty}$ functions as hyperfunctions in the framework of Čech–Dolbeault cohomology. This article aims to characterize a Čech–Dolbeault representative which corresponds to the image of the embedding of a $C^{\infty}$ function, and also to construct the inverse map of the embedding of $C^{\infty}$ functions.