Bases in spaces of analytic germs

We prove precise decomposition results and logarithmically convex estimates in certain weighted spaces of holomorphic germs near R. These imply that the spaces have a basis and are tamely isomorphic to the dual of a power series space of finite type which can be calculated in many situations. Our results apply to the Gelfand-Shilov spaces S-alpha(1) and S-1(alpha) for alpha > 0 and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.