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Results on Some Neutrix Convolutions of Functions and Distributions

Fisher, Brian, and Telci, Mustafa, (2003) Results on Some Neutrix Convolutions of Functions and Distributions. Bulletin of the Malaysian Mathematical Sciences Society, 26 (2). pp. 189-199. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v26n2/v26n2p5.pdf

Affiliations

Leicester University, Dept. of Mathematics and Computer Science
Trakya University, Dept. of Mathematics

Abstract

The neutrix convolution of two locally summable functions or distributions $f$ and $g$ is defined to be the limit of the sequence $\{f_n \ast g\}$ where $f_n(x) = f(x)\tau_n(x)$ and ${\tau_n(x)}$ is a certain function with compact support and the sequence {\tau_n} converges to the identity function on the real line. The neutrix convolution of the functions $x_+^r \ln x_+$ and $e^\lambda^x$ is evaluated for $r = 0, 1 , 2, ...$ and all $\lambda\neq 0$. Further neutrix convolutions are then deduced.

Item Type:Journal
Keywords:distribution, exponential integral, neutrix, neutrix limit, convolution, neutrix convolution
Subjects:Q Science, Computer Science
ID Code:1193

1. J.G. van der Corput, Introduction to the neutrix calculus, J. Analyse Math. (1959—60), 29 1—398.

2. Fisher, Brian Neutrices and the convolution of distributions, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 17(1987), 119—135.

3. Fisher, Brian and F. Al-Sirehy, On the cosine integral and the convolution, Stud. Cerc. St. Ser. Matematica, Universitea Bacau 9 (1999), 73—94.

4. Fisher, Brian and J.D. Nicholas, On the exponential integral, Hacet. Bull. Nat. Sci. Eng. Ser. B 28 (1999), 55—64.

5. Fisher, Brian and Telci, Mustafa Some neutrix convolutions of functions and distributions, submitted for publication.

6. I.M. Gel’fand and G.E. Shilov, Generalized Functions, Vol. I, Academic Press, 1964.

7. I.N. Sneddon, Special Functions of Mathematical Physics and Chemistry, Oliver and Boyd, 1961.

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