Solving integral equation of \(n\)-variables by \({\mathfrak L}\) and \({\mathfrak L}^{-1}\) operators. (English) Zbl 0659.44003
The author generalizes a theorem of C. Fox [Proc. Am. Math. Soc. 29, 299-306 (1971; Zbl 0215.192)] on the Laplace transform and its inverse to the case of n-variables. This theorem is used for solving an integral equation of n-variables involving the associated Bessel function \(K_{\nu}(x)\) as kernel.
Reviewer: K.N.Srivastava
MSC:
| 44A10 | Laplace transform |
| 44A30 | Multiple integral transforms |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 45H05 | Integral equations with miscellaneous special kernels |
