On the integral equation \(f(x)-(c/L(x))\int_ 0^{L(x)} f(y) dy=g(x)\) where \(L(x)=\min\{ax,1\}\), \(a>1\) (Q1353463)
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scientific article; zbMATH DE number 1005458
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the integral equation \(f(x)-(c/L(x))\int_ 0^{L(x)} f(y) dy=g(x)\) where \(L(x)=\min\{ax,1\}\), \(a>1\) |
scientific article; zbMATH DE number 1005458 |
Statements
On the integral equation \(f(x)-(c/L(x))\int_ 0^{L(x)} f(y) dy=g(x)\) where \(L(x)=\min\{ax,1\}\), \(a>1\) (English)
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24 February 1998
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A singular expansion and regularity properties for a solution of the integral equation in the title are obtained using the Mellin transform and the Fubini theorem.
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Banach fixed point theorem
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Mellin transform
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singular expansion
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regularity
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