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Bases in spaces of analytic germs

Michael Langenbruch (2012)

Annales Polonici Mathematici

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 ¹ α and S α for α > 0 and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.

Tame Köthe Sequence Spaces are Quasi-Normable

Krzysztof Piszczek (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that every tame Fréchet space admits a continuous norm and that every tame Köthe sequence space is quasi-normable.

Tameness in Fréchet spaces of analytic functions

Aydın Aytuna (2016)

Studia Mathematica

A Fréchet space with a sequence | | · | | k k = 1 of generating seminorms is called tame if there exists an increasing function σ: ℕ → ℕ such that for every continuous linear operator T from into itself, there exist N₀ and C > 0 such that | | T ( x ) | | C | | x | | σ ( n ) ∀x ∈ , n ≥ N₀. This property does not depend upon the choice of the fundamental system of seminorms for and is a property of the Fréchet space . In this paper we investigate tameness in the Fréchet spaces (M) of analytic functions on Stein manifolds M equipped with the compact-open...

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