Andreas Debrouwere

On the non-triviality of certain spaces of analytic functions. Hyperfunctions and ultrahyperfunctions of fast growth

We study function spaces consisting of analytic functions with fast decay on horizontal strips of the complex plane with respect to a given weight function. Their duals, so called spaces of (ultra)hyperfunctions of fast growth, generalize the spaces of Fourier hyperfunctions and Fourier ultrahyperfunctions. An analytic representation theory for their duals is developed and applied to characterize the non-triviality of these function spaces in terms of the growth order of the weight function. In particular, we show that the Gelfand–Shilov spaces of Beurling type

Solution to the first Cousin problem for vector-valued quasianalytic functions

\mathcal {S}^{(p!)}_{(M_p)}

Generalized Function Algebras Containing Spaces of Periodic Ultradistributions

S(Mp)(p!) and Roumieu type

A non-linear theory of infrahyperfunctions

\mathcal {S}^{\{p!\}}_{\{M_p\}}

Contributions to the linear and non-linear theory of ultradistributions

S{Mp}{p!} are non-trivial if and only if