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1
Content available remote

Spaces of Whitney jets on self-similar sets

100%
Vogt D.
Studia Mathematica
|
2013
|
tom 218
|
nr 1
89-94
EN
It is shown that complemented subspaces of s, that is, nuclear Fréchet spaces with properties (DN) and (Ω), which are 'almost normwise isomorphic' to a multiple direct sum of copies of themselves are isomorphic to s. This is applied, for instance, to spaces of Whitney jets on the Cantor set or the Sierpiński triangle and gives new results and also sheds new light on known results.
2
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Section spaces of real analytic vector bundles and a theorem of Grothendieck and Poly

100%
Vogt D.
Banach Center Publications
|
2010
|
tom 88
|
nr 1
315-321
EN
The structure of the section space of a real analytic vector bundle on a real analytic manifold X is studied. This is used to improve a result of Grothendieck and Poly on the zero spaces of elliptic operators and to extend a result of Domański and the author on the non-existence of bases to the present case.
3
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The tensor algebra of power series spaces

100%
Vogt D.
Studia Mathematica
|
2009
|
tom 193
|
nr 2
189-202
EN
The linear isomorphism type of the tensor algebra T(E) of Fréchet spaces and, in particular, of power series spaces is studied. While for nuclear power series spaces of infinite type it is always s, the situation for finite type power series spaces is more complicated. The linear isomorphism T(s) ≅ s can be used to define a multiplication on s which makes it a Fréchet m-algebra $s_{•}$. This may be used to give an algebra analogue to the structure theory of s, that is, characterize Fréchet m-algebras with (Ω) as quotient algebras of $s_{•}$ and Fréchet m-algebras with (DN) and (Ω) as quotient algebras of $s_{•}$ with respect to a complemented ideal.
4
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Non-natural topologies on spaces of holomorphic functions

100%
Vogt D.
Annales Polonici Mathematici
|
2013
|
tom 108
|
nr 3
215-217
EN
It is shown that every proper Fréchet space with weak*-separable dual admits uncountably many inequivalent Fréchet topologies. This applies, in particular, to spaces of holomorphic functions, solving in the negative a problem of Jarnicki and Pflug. For this case an example with a short self-contained proof is added.
5
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The space of real-analytic functions has no basis

64%
Domański P., Vogt D.
Studia Mathematica
|
2000
|
tom 142
|
nr 2
187-200
EN
Let Ω be an open connected subset of $ℝ^d$. We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.
6
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Construction of standard exact sequences of power series spaces

64%
Poppenberg M., Vogt D.
Studia Mathematica
|
1994-1995
|
tom 112
|
nr 3
229-241
XX
The following result is proved: Let $Λ_R^p(α)$ denote a power series space of infinite or of finite type, and equip $Λ_R^p(α)$ with its canonical fundamental system of norms, R ∈ {0,∞}, 1 ≤ p < ∞. Then a tamely exact sequence (⁎) $0 → Λ_{R}^{p}(α) → Λ_{R}^{p}(α) → Λ_{R}^{p}(α)^ℕ → 0$ exists iff α is strongly stable, i.e. $lim_n α_{2n}/α_n = 1$, and a linear-tamely exact sequence (*) exists iff α is uniformly stable, i.e. there is A such that $lim sup_n α_{Kn}/α_n ≤ A < ∞$ for all K. This result extends a theorem of Vogt and Wagner which states that a topologically exact sequence (*) exists iff α is stable, i.e. $sup_n α_{2n}/α_n < ∞$.
7
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Fréchet spaces with quotients failing the bounded approximation property

45%
Dubinsky E., Vogt D.
Studia Mathematica
|
1985
|
tom 81
|
nr 1
71-77
8
Content available remote

Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces

45%
Meise R., Vogt D.
Studia Mathematica
|
1986
|
tom 83
|
nr 2
147-166
9
Content available remote

Charakterisierung der Unterraüme und Quotienteräume der nuklearen stabilen Potenzreihenraüme von unendlichem Typ

45%
Vogt D., Wagner M. J.
Studia Mathematica
|
1981
|
tom 70
|
nr 1
63-80
10
Content available remote

Charakterisierung der Unterraüme eines nuklearen stabilen Potenzreihenraumes von endlichen Typ

44%
Vogt D.
Studia Mathematica
|
1981-1982
|
tom 71
|
nr 3
251-270
11
Content available remote

Complemented subspaces in tame power series spaces

38%
Dubinsky E., Vogt D.
Studia Mathematica
|
1989
|
tom 93
|
nr 1
71-85
12
Content available remote

Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau

32%
Vogt D., Wagner M. J.
Studia Mathematica
|
1980
|
tom 67
|
nr 3
225-240
13
Content available remote

Structure of spaces of holomorphic functions on infinite dimensional polydiscs

32%
Meise R., Vogt D.
Studia Mathematica
|
1982-1983
|
tom 75
|
nr 3
235-262
14
Content available remote

On the functors Ext¹(E,F) for Fréchet spaces

32%
Vogt D.
Studia Mathematica
|
1987
|
tom 85
|
nr 2
163-197
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