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Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space $_{(ω)} (ℝ)$ 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 $_{(ω)} [a, b]$ 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 $_{(ω)} (ℝ)$ .

Extension and lacunas of solutions of linear partial differential equations

Uwe Franken; Reinhold Meise — 1996

Annales de l'institut Fourier

Let $K \subset Q$ be compact, convex sets in $ℝ^{n}$ with $\overset{\circ}{K} \neq \emptyset$ and let $P (D)$ be a linear, constant coefficient PDO. It is characterized in various ways when each zero solution of $P (D)$ in the space $ℰ (K)$ of all $C^{\infty}$ -functions on $K$ extends to a zero solution in $ℰ (Q)$ resp. in $ℰ (ℝ^{n})$ . The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of $P$ in $ℂ^{n}$ and in terms of for $P (D)$ with lacunas.

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Darstellung temperierter vektorwertiger Distributionen durch holomorphe Funktionen I.

Rml;ume holomorpher Vektorfunktionen mit Wachstumsbedingungen und topologische Tensorprodukte.

Darstellung temperierter vektorwertiger Distributionen durch holomorphe Funktionen II.

Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals.

Sequence space representations for zero-solutions of convolution equations on ultradifferentiable functions of Roumieu type

Characterization of Convolution Operators on Spaces of C-Functions Admitting a Continuous Linear Right Inverse.

Counterexamples in Holomorphic Functions on Nuclear Fréchet Spaces.

Analytic isomorphisms of infinite dimensional polydiscs and an application

Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces

Structure of spaces of holomorphic functions on infinite dimensional polydiscs

Sequence space representations for (FN)-algebras of entire functions modulo closed ideals

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

Extension and lacunas of solutions of linear partial differential equations

Bemerkungen über die Approximationseigenschaft lokalkonvexer Funktionenräume.

Continuous linear right inverses for partial differential operators of order 2 and fundamental solutions in half spaces.

Distributionen mit Werten in topologischen Vektorräumen II.

Distributionen mit Werten in topologischen Vektorräumen I.

Lokalkonvexe Unterräume in topologischen Vektorräumen und das ...- Produkt.

Each Non-Zero Convolution Operator on the Entire Functions Admits a Continuous Linear Right Inverse.

Characterization of nuclear Fréchet spaces in which every bounded set is polar