Bases in spaces of analytic germs
Tom 106 / 2012
Annales Polonici Mathematici 106 (2012), 223-243
MSC: Primary 46A35, 46E10; Secondary 46A63, 46A61, 46F15.
DOI: 10.4064/ap106-0-18
Streszczenie
We prove precise decomposition results and logarithmically convex estimates in certain weighted spaces of holomorphic germs near $\mathbb{R}$. 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 $S^1_{\alpha}$ and $S_1^{\alpha}$ for $\alpha>0$ and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.