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On inversion of \(H\)-transform in \({\mathfrak L}_{v,r}\)-space. (English) Zbl 0912.33005
This paper deals with the inversion of an integral transform of a function \(f\) when the kernel is a general \(H\)-function and when \(f\) satisfies the condition \[ \int^\infty_0 \bigl| t^\nu f(t)\bigr|^r {dt\over t} <\infty,\;1<r< \infty,\;\nu\text{ real}. \] Inversion theorems are obtained for various situations involving the parameters. The main results are entensions of the corresponding results when the kernel is a \(G\)-function, obtained by P. G. Rooney [Proc. R. Soc. Edinb. Sect. A 93, 265-297 (1983; Zbl 0509.44001)].

MSC:
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
44A20 Integral transforms of special functions
Keywords:
\(G\)-function
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