Convolution operators in infinite dimension.

Nguyen Van Khue; Nguyen Dinh Sang

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Displaying similar documents to “Convolution operators in infinite dimension.”

Convolution operators on the space of holomorphic germs of nuclear type

Azevedo Biagioni, H. (1983-1984)

Portugaliae mathematica

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Surjective convolution operators on spaces of distributions.

Leonhard Frerick, Jochen Wengenroth (2003)

RACSAM

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We review recent developments in the theory of inductive limits and use them to give a new and rather easy proof for Hörmander?s characterization of surjective convolution operators on spaces of Schwartz distributions.

Continuous linear right inverses for convolution operators in spaces of real analytic functions

Michael Langenbruch (1994)

Studia Mathematica

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We determine the convolution operators $T_{μ} : = μ *$ on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z).

Holomorphy types and spaces of entire functions of bounded type on Banach spaces

Vinícius V. Fávaro, Ariosvaldo M. Jatobá (2009)

Czechoslovak Mathematical Journal

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In this paper spaces of entire functions of $Θ$ -holomorphy type of bounded type are introduced and results involving these spaces are proved. In particular, we “construct an algorithm” to obtain a duality result via the Borel transform and to prove existence and approximation results for convolution equations. The results we prove generalize previous results of this type due to B. Malgrange: Existence et approximation des équations aux dérivées partielles et des équations des convolutions....

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

Jóse Bonet, Antonio Galbis, R. Meise (1997)

Studia Mathematica

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Let $ℇ_{(ω)} (Ω)$ denote the non-quasianalytic class of Beurling type on an open set Ω in $ℝ^{n}$ . For $μ \in ℇ_{(ω)}^{'} (ℝ^{n})$ the surjectivity of the convolution operator $T_{μ} : ℇ_{(ω)} (Ω_{1}) \to ℇ_{(ω)} (Ω_{2})$ 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 $S_{μ} : D_{ω}^{'} (Ω_{1}) \to D_{ω}^{'} (Ω_{2})$ between ultradistributions of Roumieu type whenever...

On the convolution in the space $𝒟_{L^{2}}^{' (M_{p})}$

Stevan Pilipović (1988)

Rendiconti del Seminario Matematico della Università di Padova

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On the space of convolution operators in $K_{1}^{'}$

Z. Zieleźny (1968)

Studia Mathematica

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Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type

Thomas Meyer (1997)

Studia Mathematica

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Let $ε_{ω} (I)$ denote the space of all ω-ultradifferentiable functions of Roumieu type on an open interval I in ℝ. In the special case ω(t) = t we get the real-analytic functions on I. For $μ \in ε_{ω} {(I)}^{'}$ with $s u p p (μ) = 0$ one can define the convolution operator $T_{μ} : ε_{ω} (I) \to ε_{ω} (I)$ , $T_{μ} (f) (x) : = ⟨ μ, f (x - \cdot) ⟩$ . We give a characterization of the surjectivity of $T_{μ}$ for quasianalytic classes $ε_{ω} (I)$ , where I = ℝ or I is an open, bounded interval in ℝ. This characterization is given in terms of the distribution of zeros of the Fourier Laplace transform $\hat{μ}$ of μ.

Solution operators for convolution equations on the germs of analytic functions on compact convex sets in $ℂ^{N}$

S. Melikhov, Siegfried Momm (1995)

Studia Mathematica

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$G \subset ℂ^{N}$ is compact and convex it is known for a long time that the nonzero constant coefficients linear partial differential operators (of finite or infinite order) are surjective on the space of all analytic functions on G. We consider the question whether solutions of the inhomogeneous equation can be given in terms of a continuous linear operator. For instance we characterize those sets G for which this is always the case.