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### A characterization of the space ${D}_{F}^{\text{'}}$

Matematički Vesnik

### A commutative neutrix convolution of distributions and the exchange formula

Archivum Mathematicum

### A comparison on the commutative neutrix convolution of distributions and the exchange formula

Czechoslovak Mathematical Journal

Let $\stackrel{˜}{f}$, $\stackrel{˜}{g}$ be ultradistributions in ${𝒵}^{\text{'}}$ and let ${\stackrel{˜}{f}}_{n}=\stackrel{˜}{f}*{\delta }_{n}$ and ${\stackrel{˜}{g}}_{n}=\stackrel{˜}{g}*{\sigma }_{n}$ where $\left\{{\delta }_{n}\right\}$ is a sequence in $𝒵$ which converges to the Dirac-delta function $\delta$. Then the neutrix product $\stackrel{˜}{f}\diamond \stackrel{˜}{g}$ is defined on the space of ultradistributions ${𝒵}^{\text{'}}$ as the neutrix limit of the sequence $\left\{\frac{1}{2}\left({\stackrel{˜}{f}}_{n}\stackrel{˜}{g}+\stackrel{˜}{f}{\stackrel{˜}{g}}_{n}\right)\right\}$ provided the limit $\stackrel{˜}{h}$ exist in the sense that $\underset{n\to \infty }{\mathrm{N}\text{-}lim}\frac{1}{2}〈{\stackrel{˜}{f}}_{n}\stackrel{˜}{g}+\stackrel{˜}{f}{\stackrel{˜}{g}}_{n},\psi 〉=〈\stackrel{˜}{h},\psi 〉$ for all $\psi$ in $𝒵$. We also prove that the neutrix convolution product $f♦\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}*\phantom{\rule{0.166667em}{0ex}}g$ exist in ${𝒟}^{\text{'}}$, if and only if the neutrix product $\stackrel{˜}{f}\diamond \stackrel{˜}{g}$ exist in ${𝒵}^{\text{'}}$ and the exchange formula $F\left(f♦\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}*\phantom{\rule{0.166667em}{0ex}}g\right)=\stackrel{˜}{f}\diamond \stackrel{˜}{g}$ is then satisfied.

### A contribution to the equivalence results for the product of distributions

Commentationes Mathematicae Universitatis Carolinae

Products $\left[S\right]·\left[T\right]$ and $\left[S\right]·T$, defined by model delta-nets, are equivalent.

### A convolution product of $\left(2j\right)$th derivative of Dirac's delta in $r$ and multiplicative distributional product between ${r}^{-k}$ and $\nabla \left({▵}^{j}\delta \right)$.

International Journal of Mathematics and Mathematical Sciences

### A distributional representation of strip analytic functions.

International Journal of Mathematics and Mathematical Sciences

### A distributional summation formula of Euler-MacLaurin type in two variables.

Divulgaciones Matemáticas

### A functional equation of Aczél and Chung in generalized functions.

Advances in Difference Equations [electronic only]

### A Note on Multipliers for Integrable Boehmians

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 44A40, 42A38, 46F05The product of an entire function satisfying a growth condition at infinity and an integrable Boehmian is defined. Properties of this product are investigated.

### A note on the convolution and the product ${𝒟}^{\text{'}}$ and ${𝒮}^{\text{'}}$.

International Journal of Mathematics and Mathematical Sciences

### A note on the convolution in the Mellin sense with generalized functions.

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

### A note on the spaces ${𝒪}_{M}$ and ${𝒪}_{M}^{\text{'}}$.

International Journal of Mathematics and Mathematical Sciences

### A proof of the theorem of supports

Studia Mathematica

### A remark on singular supports of convolutions.

Mathematica Scandinavica

### A sequential theory of some semigroups in special spaces of generalized functions

Matematički Vesnik

### A Singular Convolution Equation In The Space Of Distributions

Publications de l'Institut Mathématique

### A singular convolution equation in the space of distributions.

Publications de l'Institut Mathématique [Elektronische Ressource]

### A structural theorem for distributions having S-asymptotic.

Publications de l'Institut Mathématique. Nouvelle Série

### A Tauberian theorem for distributions

Commentationes Mathematicae Universitatis Carolinae

The well-known general Tauberian theorem of N. Wiener is formulated and proved for distributions in the place of functions and its Ganelius' formulation is corrected. Some changes of assumptions of this theorem are discussed, too.

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