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1
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Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse

100%
Bonet J., Meise R.
Studia Mathematica
|
2008
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tom 184
|
nr 1
49-77
EN
Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space $𝓔_{(ω)}(ℝ)$ of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on $𝓔_{(ω)} [a, b]$ for each compact interval [a,b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on $𝓔_{(ω)}(ℝ)$.
2
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Köthe coechelon spaces as locally convex algebras

100%
Bonet J., Domański P.
Studia Mathematica
|
2010
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tom 199
|
nr 3
241-265
EN
We study those Köthe coechelon sequence spaces $k_{p}(V)$, 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix V = (vₙ)ₙ when an algebra $k_{p}(V)$ is unital, locally m-convex, a 𝒬-algebra, has a continuous (quasi)-inverse, all entire functions act on it or some transcendental entire functions act on it. It is proved that all multiplicative functionals are continuous and a precise description of all regular and all degenerate maximal ideals is given even for arbitrary solid algebras of sequences with pointwise multiplication. In particular, it is shown that all regular maximal ideals are solid.
3
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Weighted $L^{∞}$-estimates for Bergman projections

81%
Bonet J., Engliš M., Taskinen J.
Studia Mathematica
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2005
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tom 171
|
nr 1
67-92
EN
We consider Bergman projections and some new generalizations of them on weighted $L^{∞}(𝔻)$-spaces. A new reproducing formula is obtained. We show the boundedness of these projections for a large family of weights v which tend to 0 at the boundary with a polynomial speed. These weights may even be nonradial. For logarithmically decreasing weights bounded projections do not exist. In this case we instead consider the projective description problem for holomorphic inductive limits.
4
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Characterizing Fréchet-Schwartz spaces via power bounded operators

81%
Albanese A., Bonet J., Ricker W.
Studia Mathematica
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2014
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tom 224
|
nr 1
25-45
EN
We characterize Köthe echelon spaces (and, more generally, those Fréchet spaces with an unconditional basis) which are Schwartz, in terms of the convergence of the Cesàro means of power bounded operators defined on them. This complements similar known characterizations of reflexive and of Fréchet-Montel spaces with a basis. Every strongly convergent sequence of continuous linear operators on a Fréchet-Schwartz space does so in a special way. We single out this type of "rapid convergence" for a sequence of operators and study its relationship to the structure of the underlying space. Its relevance for Schauder decompositions and the connection to mean ergodic operators on Fréchet-Schwartz spaces is also investigated.
5
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Projective representations of spaces of quasianalytic functionals

81%
Bonet J., Meise R., Melikhov S.
Studia Mathematica
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2004
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tom 164
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nr 1
91-102
EN
The weighted inductive limit of Fréchet spaces of entire functions in N variables which is obtained as the Fourier-Laplace transform of the space of analytic functionals on an open convex subset of $ℝ^{N}$ can be described algebraically as the intersection of a family of weighted Banach spaces of entire functions. The corresponding result for the spaces of quasianalytic functionals is also derived.
6
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Extension of vector-valued holomorphic and harmonic functions

81%
Bonet J., Frerick L., Jordá E.
Studia Mathematica
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2007
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tom 183
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nr 3
225-248
EN
We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak*-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.
7
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Associated weights and spaces of holomorphic functions

81%
Bierstedt K. D., Bonet J., Taskinen J.
Studia Mathematica
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1998
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tom 127
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nr 2
137-168
EN
When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset $G ⊂ ℂ^N$ which play an important role in the projective description problem. A number of relevant examples are provided, and a "new projective description problem" is posed. The proof of our main result can also serve to characterize when the embedding of two weighted Banach spaces of holomorphic functions is compact. Our investigations on conditions when an associated weight coincides with the original one and our estimates of the associated weights in several cases (mainly for G = ℂ or D) should be of independent interest.
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