Bases in spaces of analytic germs

Tom 106 / 2012

Michael Langenbruch Annales Polonici Mathematici 106 (2012), 223-243 MSC: Primary 46A35, 46E10; Secondary 46A63, 46A61, 46F15. DOI: 10.4064/ap106-0-18


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.


  • Michael LangenbruchInstitute of Mathematics
    University of Oldenburg
    D-26111 Oldenburg, Germany

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