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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The solution of an integral equation


Author: C. Nasim
Journal: Proc. Amer. Math. Soc. 40 (1973), 95-101
MSC: Primary 45H05
MathSciNet review: 0320665
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Abstract: Various methods are developed to solve the integral equation $ f(x) = \int_0^\infty {g(t)} k(xt)dt$, when the Mellin transform $ K(s)$ of the kernel function $ k(x)$ is decomposable. Each method corresponds to the way $ K(s)$ is decomposed: Namely (i) $ K(s) = 1/L(1 - s)M(1 - s)$, (ii) $ K(s) = H(s)/M(1 - s)$ and (iii) $ K(s) = N(s)H(s)$, where $ L,M,N$ and $ H$ are arbitrary functions of the complex variable $ s$. Numerous special cases and examples are given to illustrate the technique and the advantage of these methods.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0320665-6
PII: S 0002-9939(1973)0320665-6
Keywords: Fourier transform, Fourier kernel, Mellin transform, the Parseval Theorem, $ {L^2}$-space, convergence in mean, Laplace and Stieltjes integral equations, Bessel functions
Article copyright: © Copyright 1973 American Mathematical Society