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On the support of Fourier transform of weighted distributions

Martha Guzmán-Partida (2010)

Commentationes Mathematicae Universitatis Carolinae

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 ≥ 0 and x 2 ≥ 0 .

One-parameter semigroups in the convolution algebra of rapidly decreasing distributions

(2012)

Colloquium Mathematicae

The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra C ' ( ℝ ⁿ ; M m × m ) of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that G ∈ C ' ( ℝ ⁿ ; M m × m ) is the generating distribution of an i.d.c.s. if and only if the operator ∂ t ⊗ m × m - G ∗ on ℝ 1 + n satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.

Operational calculus and Fourier transform on Boehmians

V. Karunakaran, R. Roopkumar (2005)

Colloquium Mathematicae

We define various operations on the space of ultra Boehmians like multiplication with certain analytic functions which are Fourier transforms of compactly supported distributions, polynomials, and characters ( e i s t , s , t ∈ ℝ ) , translation, differentiation. We also prove that the Fourier transform on the space of ultra Boehmians has all the operational properties as in the classical theory.

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