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

José BonetReinhold Meise — 2008

Studia Mathematica

Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space ( ω ) ( ) 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 ( 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 ( ω ) ( ) .

Köthe coechelon spaces as locally convex algebras

José BonetPaweł Domański — 2010

Studia Mathematica

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 -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...

Inductive duals of distinguished frechet spaces

José BonetSusanne Dierolf — 1996

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

The purpose of this note is to give an example of a distinguished Fréchet space and a non-distinguished Fréchet space which have the same inductive dual. Accordingly, distinguishedness is a property which is not reflected in the inductive dual. In contrast to this example, it was known that the properties of being quasinormable or having the density condition can be characterized in terms of the inductive dual of a Fréchet space.

On the range of convolution operators on non-quasianalytic ultradifferentiable functions

Jóse BonetAntonio GalbisR. Meise — 1997

Studia Mathematica

Let ( ω ) ( Ω ) denote the non-quasianalytic class of Beurling type on an open set Ω in n . For μ ( ω ) ' ( n ) the surjectivity of the convolution operator T μ : ( ω ) ( Ω 1 ) ( ω ) ( Ω 2 ) is characterized by various conditions, e.g. in terms of a convexity property of the pair ( Ω 1 , Ω 2 ) and the existence of a fundamental solution for μ or equivalently by a slowly decreasing condition for the Fourier-Laplace transform of μ. Similar conditions characterize the surjectivity of a convolution operator S μ : D ω ' ( Ω 1 ) D ω ' ( Ω 2 ) between ultradistributions of Roumieu type whenever μ ω ' ( n ) . These...

Associated weights and spaces of holomorphic functions

Klaus BierstedtJosé BonetJari Taskinen — 1998

Studia Mathematica

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 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...

Weighted L -estimates for Bergman projections

José BonetMiroslav EnglišJari Taskinen — 2005

Studia Mathematica

We consider Bergman projections and some new generalizations of them on weighted L ( ) -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.

Extension of vector-valued holomorphic and harmonic functions

José BonetLeonhard FrerickEnrique Jordá — 2007

Studia Mathematica

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.

Biduality in (LF)-spaces.

Klaus D. BierstedtJosé Bonet — 2001


En la Sección 1 se pueban resultados abstractos sobre preduales y sobre bidualidad de espacios (LF). Sea E = ind E un espacio (LF), ponemos H = ind H para una sucesión de subespacios de Fréchet H de E con H ⊂ H. Investigamos bajo qué condiciones el espacio E es canónicamente (topológicamente isomorfo a) el bidual inductivo (H')' o (incluso) al bidual fuerte de H. Los resultados abstractos se aplican en la Sección 2, especialmente a espacios (LF) ponderados de funciones holomorfas, pero también a...

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