## On the sheaf of Laplace hyperfunctions with holomorphic parameters

J. Math. Sci. Univ. Tokyo
Vol. 19 (2012), No. 4, Page 559–586.

Honda, Naofumi ; Umeta, Kohei
On the sheaf of Laplace hyperfunctions with holomorphic parameters
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Abstract:
We give a vanishing theorem of cohomology groups on a pseudoconvex open subset for holomorphic functions with exponential growth at infinity. As an application, we construct the sheaf of Laplace hyperfunctions and that with holomorphic parameters, and we also study several properties of these sheaves .

Keywords: Laplace hyperfunctions, Laplace transform, holomorphic functions of exponential type, sheaves, cohomology.

Mathematics Subject Classification (2010): Primary 32A45; Secondary 44A10.
Mathematical Reviews Number: MR3086747