\(L^1\)-approximation to Laplace transforms of signed measures (Q719505)
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scientific article; zbMATH DE number 5956050
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^1\)-approximation to Laplace transforms of signed measures |
scientific article; zbMATH DE number 5956050 |
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\(L^1\)-approximation to Laplace transforms of signed measures (English)
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10 October 2011
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This work deals with the construction of interpolation by entire functions to functions that are piecewise equal to one-sided Laplace transforms of signed measures. The interpolating points are the zeros of Laguerre-Polya entire functions. The author shows that if the interpolating function is sufficiently regular then the interpolate is also the best \(L^1\)-approximation from the family of functions of fixed exponential type.
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exponential type
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best approximation
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variation diminishing
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extremal functions
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entire functions
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