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Let A be the class of all real-analytic functions and β the class of all Boehmians. We show that there is no continuous operation on β which is ordinary multiplication when restricted to A.

The product of distributions on $R^{m}$

Cheng Lin-Zhi, Brian Fisher (1992)

Commentationes Mathematicae Universitatis Carolinae

The fixed infinitely differentiable function $ρ (x)$ is such that ${n ρ (n x)}$ is a regular sequence converging to the Dirac delta function $δ$ . The function $δ_{𝐧} (𝐱)$ , with $𝐱 = (x_{1}, \dots, x_{m})$ is defined by $δ_{𝐧} (𝐱) = n_{1} ρ (n_{1} x_{1}) \dots n_{m} ρ (n_{m} x_{m}) .$ The product $f \circ g$ of two distributions $f$ and $g$ in $𝒟_{m}^{'}$ is the distribution $h$ defined by $\underset{n_{1} \to \infty}{error} \dots \underset{n_{m} \to \infty}{error} 〈 f_{𝐧} g_{𝐧}, φ 〉 = 〈 h, φ 〉,$ provided this neutrix limit exists for all $φ (𝐱) = φ_{1} (x_{1}) \dots φ_{m} (x_{m})$ , where $f_{𝐧} = f * δ_{𝐧}$ and $g_{𝐧} = g * δ_{𝐧}$ .

The product of $r^{- k}$ and $\nabla δ$ on $ℝ^{m}$ .

Li, C.K. (2000)

International Journal of Mathematics and Mathematical Sciences

The pseudodifferential operator $A (x, D)$ .

Pathak, R.S., Pathak, S. (2004)

International Journal of Mathematics and Mathematical Sciences

The Quasiasymptotic Expansion and the Moment Expansion of Tempered Distributions

D. Nikolić-Despotović, Stevan Pilipović (1993)

Publications de l'Institut Mathématique

The regularity of convolution and restriction of distributions

Ryszard Wawak (1988)

Annales Polonici Mathematici

The sequential approach to the product of distribution.

Li, C.K. (2001)

International Journal of Mathematics and Mathematical Sciences

The space $D (U)$ is not $B_{r}$ -complete

Manuel Valdivia (1977)

Annales de l'institut Fourier

Certain classes of locally convex space having non complete separated quotients are studied and consequently results about $B_{r}$ -completeness are obtained. In particular the space of L. Schwartz $D (Ω)$ is not $B_{r}$ -complete where $Ω$ denotes a non-empty open set of the euclidean space $R^{m}$ .

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Displaying 41 – 60 of 89

The multiplication functions of Kučera

The $n$ -dimensional continuous wavelet transformation on Gelfand and Shilov type spaces.

The $n$ -field-irreducible part of a $n$ -point functional

The n-dimensional distributional Mellin transformation.

The neutrix convolution product in $Z^{'} (m)$ and the exchange formula.

The Neutrix Convolution Product x -r,- ○ x μ,+

The neutrix product of the distributions $x_{+}^{λ} ln x_{+}$ and $x_{-}^{- λ - r}$ .

The non-Archimedean Laplace transform.

The prime number theorem for Beurling's generalized numbers. New cases

The product of a function and a Boehmian

The product of distributions on $R^{m}$

The product of $r^{- k}$ and $\nabla δ$ on $ℝ^{m}$ .

The pseudodifferential operator $A (x, D)$ .

The Quasiasymptotic Expansion and the Moment Expansion of Tempered Distributions

The regularity of convolution and restriction of distributions

The sequential approach to the product of distribution.

The space $D (U)$ is not $B_{r}$ -complete

The Space of Distributions D' (...) is not Br- Complete.

The space of Laplace transformable distributions

The spaces $𝒪_{M}$ and $𝒪_{C}$ are ultrabornological. A new proof.

Currently displaying 41 – 60 of 89