Lifting-Probleme für Vektorfunktionen und ...-Sequenzen.
A splitting theory for the space of distributions
The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'
Continuous linear right inverses for partial differential operators of order 2 and fundamental solutions in half spaces.
Extremal plurisubharmonic functions of linear growth on algebraic varieties.
Entire functions on nuclear sequence spaces.
Standard exact projective resolutions relative to a countable class of Fréchet spaces
We will show that for each sequence of quasinormable Fréchet spaces there is a Köthe space λ such that and there are exact sequences of the form . If, for a fixed ℕ, is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form . The result has some applications in the theory of the functor in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.
Fréchet quotients of spaces of real-analytic functions
We characterize all Fréchet quotients of the space (Ω) of (complex-valued) real-analytic functions on an arbitrary open set . We also characterize those Fréchet spaces E such that every short exact sequence of the form 0 → E → X → (Ω) → 0 splits.
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