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A class of distributions supported by certain noncompact regular sets K are identified with continuous linear functionals on $C_{0}^{\infty} (K)$ . The proof is based on a parameter version of the Seeley extension theorem.

Characterization of regular tempered distributions

Zofia Szmydt (1983)

Annales Polonici Mathematici

Characterization of some Subspaces of (D') by S-asymptotic

Bogoljub Stanković (1987)

Publications de l'Institut Mathématique

Characterization of surjective convolution operators on Sato's hyperfunctions

Michael Langenbruch (2010)

Banach Center Publications

Let $μ \in {(ℝ^{d})}^{'}$ be an analytic functional and let $T_{μ}$ be the corresponding convolution operator on Sato’s space $(ℝ^{d})$ of hyperfunctions. We show that $T_{μ}$ is surjective iff $T_{μ}$ admits an elementary solution in $(ℝ^{d})$ iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are $0 \neq μ \in {(ℝ^{d})}^{'}$ such that $T_{μ}$ is not surjective on $(ℝ^{d})$ .

Characterization of surjective partial differential operators on spaces of real analytic functions

Michael Langenbruch (2004)

Studia Mathematica

Let A(Ω) denote the real analytic functions defined on an open set Ω ⊂ ℝⁿ. We show that a partial differential operator P(D) with constant coefficients is surjective on A(Ω) if and only if for any relatively compact open ω ⊂ Ω, P(D) admits (shifted) hyperfunction elementary solutions on Ω which are real analytic on ω (and if the equation P(D)f = g, g ∈ A(Ω), may be solved on ω). The latter condition is redundant if the elementary solutions are defined on conv(Ω). This extends and improves previous...

Characterization of the Colombeau product of distributions

Jiří Jelínek (1986)

Commentationes Mathematicae Universitatis Carolinae

Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse

B. A. Taylor, R. Meise, Dietmar Vogt (1990)

Annales de l'institut Fourier

Solving a problem of L. Schwartz, those constant coefficient partial differential operators $P (D)$ are characterized that admit a continuous linear right inverse on $ℰ (Ω)$ or $𝒟^{'} (Ω)$ , $Ω$ an open set in $R^{n}$ . For bounded $Ω$ with $C^{1}$ -boundary these properties are equivalent to $P (D)$ being very hyperbolic. For $Ω = R^{n}$ they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial $P$ .

Characterization of the range of the Radon transform on homogeneous trees.

Tarabusi, Enrico Casadio, Cohen, Joel M., Colonna, Flavia (1999)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Characterization of the $ω$ hypoelliptic convolution operators on ultradistributions.

Bonet, J., Fernández, C., Meise, R. (2000)

Annales Academiae Scientiarum Fennicae. Mathematica

Classes $K^{s}$ du type Sobolev

Mirella Krée (1974/1975)

Séminaire Paul Krée

Classes $L^{p}$ de protenseurs distributions contravariants

Paul Krée (1974/1975)

Séminaire Paul Krée

Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives

Paweł Domański (2004)

Banach Center Publications

This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...

Coefficients généralisés de séries principales sphériques et distributions sphériques sur G.../G... .

P. Delorme (1991)

Inventiones mathematicae

Colombeau product of currents

Jiří Jelínek (2005)

Commentationes Mathematicae Universitatis Carolinae

Colombeau product of de Rham's currents coincides with generalized Itano one. Sufficient conditions are found under which it is diffeomorphism invariant.

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