The solution of an integral equation
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- by C. Nasim PDF
- Proc. Amer. Math. Soc. 40 (1973), 95-101 Request permission
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.References
- Charles Fox, Solving integral equations by $L$ and $L^{-1}$ operators, Proc. Amer. Math. Soc. 29 (1971), 299–306. MR 280944, DOI 10.1090/S0002-9939-1971-0280944-6 E. C. Titchmarsh, Theory of Fourier integral, Clarendon Press, Oxford, 1937. A. Erdélyi et al., Tables of integral transforms. Vol. 1, McGraw-Hill, New York, 1954. MR 15, 868. I. S. Gradšteǐn and I. M. Ryžik, Tables of integrals, series and products, Fizmatgiz, Moscow, 1963; English transl., Academic Press, New York, 1965. MR 28 #5198; MR 33 #5952.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 95-101
- MSC: Primary 45H05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0320665-6
- MathSciNet review: 0320665