Displaying similar documents to “On the convolution in the space 𝒟 L 2 ' ( M p ) ”

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).

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 ∈ ε ω ( I ) ' with s u p p ( μ ) = 0 one can define the convolution operator T μ : ε ω ( I ) → ε ω ( I ) , T μ ( f ) ( x ) : = ⟨ μ , f ( x - · ) ⟩ . 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 μ ^ of μ.

A limit theorem for the q-convolution

Anna Kula (2011)

Banach Center Publications

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The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...