On the incomplete gamma function and the neutrix convolution

Brian Fisher; Biljana Jolevska-Tuneska; Arpad Takači

Displaying similar documents to “On the incomplete gamma function and the neutrix convolution”

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S. R. Yadava (1972)

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Extensions of two theorems on the neutrix convolution product of distributions

Brian Fisher (1991)

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

Brian Fisher, Emin Özcag (1991)

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

Adem Kiliçman (2001)

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Let $\tilde{f}$ , $\tilde{g}$ be ultradistributions in $𝒵^{'}$ and let ${\tilde{f}}_{n} = \tilde{f} * δ_{n}$ and ${\tilde{g}}_{n} = \tilde{g} * σ_{n}$ where ${δ_{n}}$ is a sequence in $𝒵$ which converges to the Dirac-delta function $δ$ . Then the neutrix product $\tilde{f} ⋄ \tilde{g}$ is defined on the space of ultradistributions $𝒵^{'}$ as the neutrix limit of the sequence ${\frac{1}{2} ({\tilde{f}}_{n} \tilde{g} + \tilde{f} {\tilde{g}}_{n})}$ provided the limit $\tilde{h}$ exist in the sense that $\underset{n \to \infty}{N - l i m} \frac{1}{2} 〈 {\tilde{f}}_{n} \tilde{g} + \tilde{f} {\tilde{g}}_{n}, ψ 〉 = 〈 \tilde{h}, ψ 〉$ for all $ψ$ in $𝒵$ . We also prove that the neutrix convolution product $f ♦ * g$ exist in $𝒟^{'}$ , if and only if the neutrix product $\tilde{f} ⋄ \tilde{g}$ exist in $𝒵^{'}$ and the exchange formula $F (f ♦ * g) = \tilde{f} ⋄ \tilde{g}$ is then satisfied.

Convolution in Colombeau's spaces of generalized functions. II: The convolution in $𝒢_{a}$ .

Nedeljkov, M., Pilipović, S. (1992)

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Convolution in Colombeau's Spaces of Generalized Functions; Part II: the Convolution in Ga

Marko Nedeljkov, Stevan Pilipović (1992)

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Convolution in Colombeau's spaces of generalized functions. II: The convolution in $𝒢_{a}$ .

Nedeljkov, M., Pilipović, S. (1992)

Publications de l'Institut Mathématique. Nouvelle Série

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A numerical constant associated with generalized convolutions

Kazimierz Urbanik (1987)

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Compact convolution operators between $L_{p} (G)$ -spaces

G. Crombez, W. Govaerts (1978)

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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...