Fourier transformation and stability of a differential equation on \(L^1(\mathbb{R})\) (Q1980370)
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scientific article; zbMATH DE number 7392332
| Language | Label | Description | Also known as |
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| English | Fourier transformation and stability of a differential equation on \(L^1(\mathbb{R})\) |
scientific article; zbMATH DE number 7392332 |
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Fourier transformation and stability of a differential equation on \(L^1(\mathbb{R})\) (English)
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8 September 2021
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Summary: In the present paper, by the Fourier transform, we show that every linear differential equation with constant coefficients of \(n\)-th order has a solution in \(L^1(\mathbb{R})\) which is infinitely differentiable in \(\mathbb{R}\smallsetminus \{0\}\). Moreover the Hyers-Ulam stability of such equations on \(L^1(\mathbb{R})\) is investigated.
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Fourier transform
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Hyers-Ulam stability
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