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Displaying 21 – 34 of 34

On the Fourier transform, Boehmians, and distributions

Dragu Atanasiu, Piotr Mikusiński (2007)

Colloquium Mathematicae

We introduce some spaces of generalized functions that are defined as generalized quotients and Boehmians. The spaces provide simple and natural frameworks for extensions of the Fourier transform.

On the orders of the extensions of linear functionals to distributions

P. Mankiewicz (1973)

Studia Mathematica

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

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

Studia Mathematica

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 $μ \in ℇ_{ω}^{'} (ℝ^{n})$ . These...

We give sufficient conditions for the support of the Fourier transform of a certain class of weighted integrable distributions to lie in the region $x_{1} \geq 0$ and $x_{2} \geq 0$ .

Displaying 21 – 34 of 34

On the Fourier transform, Boehmians, and distributions

On the orders of the extensions of linear functionals to distributions

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

On the singular support of distributions and Fourier transforms on symmetric spaces

On the space D'(l) of sequential distributions.

On the structure of certain ultradistributions.

On the structure of the ultradistributions of Beurling type.

On the support of Fourier transform of weighted distributions

On the ultradistributions of Beurling type.

On the value of a distribution at a point

On the Value of a Distribution at a Point.

On vector-valued Hörmander-Beurling spaces.

On Well-Located Subspaces of Distribution-Spaces.

Ondelettes et espaces de Besov.

Currently displaying 21 – 34 of 34