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Some commutative neutrix convolution products of functions

Brian Fisher, Adem Kiliçman (1995)

Commentationes Mathematicae Universitatis Carolinae

The commutative neutrix convolution product of the locally summable functions ${cos}_{-} (λ x)$ and ${cos}_{+} (μ x)$ is evaluated. Further similar commutative neutrix convolution products are evaluated and deduced.

Some distributional products with relativistic invariance.

Sarrico, C.O.R. (1994)

Portugaliae Mathematica

Some inequalities arising from vector-valued Dirac deltas.

M. T. Menárguez, J.L. Torrea (1998)

Mathematica Scandinavica

Some properties of the quasiasymptotic of Schwartz distributions. I: Quasiasymptotic at $\pm \infty$ .

Pilipović, Stevan (1988)

Publications de l'Institut Mathématique. Nouvelle Série

Some Properties of the Quasiasymptotic of Schwartz Distributions Part ii: Quasiasymptotic at 0

Stevan Pilipović (1988)

Publications de l'Institut Mathématique

Some remarks on convolution equations

C. A. Berenstein, M. A. Dostal (1973)

Annales de l'institut Fourier

Using a description of the topology of the spaces $E^{'} (Ω)$ ( $Ω$ open convex subset of $R^{n}$ ) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution $T$ , $T \in E^{'}$ . We give applications to a class of distributions $T$ satisfying $cv. sing. supp. S * T = cv. sing. supp. S + cv. sing. supp. T$ for all $S \in E^{'}$ .

Some results on the composition of distributions.

Fisher, Brian, Nicholas, Joel D. (2002)

Novi Sad Journal of Mathematics

Some results on the non-commutative neutrix product of distributions and $Γ^{(r)} (x)$ .

Kilicman, Adem (2000)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Some results on the product of distributions and the change of variable

Emin Özçag, Brian Fisher (1991)

Commentationes Mathematicae Universitatis Carolinae

Let $F$ and $G$ be distributions in $𝒟^{'}$ and let $f$ be an infinitely differentiable function with $f^{'} (x) > 0$ , (or $< 0$ ). It is proved that if the neutrix product $F \circ G$ exists and equals $H$ , then the neutrix product $F (f) \circ G (f)$ exists and equals $H (f)$ .

Spectral synthesis and the Pompeiu problem

L. Brown, B. Schreiber, B. A. Taylor (1973)

Annales de l'institut Fourier

It is shown that every closed rotation and translation invariant subspace $V$ of $C (R^{n})$ or $δ (R^{n})$ , $n \geq 2$ , is of spectral synthesis, i.e. $V$ is spanned by the polynomial-exponential functions it contains. It is a classical problem to find those measures $μ$ of compact support on $R^{2}$ with the following property: (P) The only function $f \in C (R^{2})$ satisfying $\int_{R^{2}} f \circ σ d μ = 0$ for all rigid motions $σ$ of $R^{2}$ is the zero function. As an application of the above result a characterization of such measures is obtained in terms of their Fourier-Laplace transforms....