A class of convolution integral equations concerning a generalized polynomial set (Q2739275)
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scientific article; zbMATH DE number 1643742
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A class of convolution integral equations concerning a generalized polynomial set |
scientific article; zbMATH DE number 1643742 |
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24 March 2002
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convolution integral equation
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Mellin transform
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Fox's \(H\)-function
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A class of convolution integral equations concerning a generalized polynomial set (English)
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The authors motivated by a recent paper of \textit{R. Srivastava} [J. Math. Anal. Appl. 186, 11-20 (1994; Zbl 0803.45005)] find inversion of the convolution type integral NEWLINE\[NEWLINEg(x)=\int^y_0 h\left( {x\over y}\right) f(y){dy \over y} (x>0),NEWLINE\]NEWLINE where \(g\) is some prescribed function, \(f\) is an unknown function and the kernel \(h\) is taken to be a certain generalized set of polynomials. Quite familiar methods of Mellin transform are applied in finding the inversion. Some corollaries of the main result are also given.
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