Fourier transformation and stability of a differential equation on \(L^1(\mathbb{R})\)
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.
scientific article; zbMATH DE number 7392332
scientific article