For ultrabornological PLS-spaces E, a theory of E-valued Fourier hyperfunctions exists if and only if E has property (PA); the hyperfunctions are realized as sheaves of compactly supported functionals and as boundary values of slowly increasing holomorphic functions.
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Vector-valued Fourier hyperfunctions and boundary values
For ultrabornological PLS-spaces E, a theory of E-valued Fourier hyperfunctions exists if and only if E has property (PA); the hyperfunctions are realized as sheaves of compactly supported functionals and as boundary values of slowly increasing holomorphic functions.