Integration of ordinary linear differential equations by Laplace-Stieltjes transforms

D’Archangelo, James; Hartman, Philip

doi:10.1090/S0002-9947-1975-0357935-8

Integration of ordinary linear differential equations by Laplace-Stieltjes transforms
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by James D’Archangelo and Philip Hartman

Trans. Amer. Math. Soc. 204 (1975), 245-266

DOI: https://doi.org/10.1090/S0002-9947-1975-0357935-8

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Abstract:

Let $R$ be a constant $N \times N$ matrix and $g(t)$ an $N \times N$ matrix of functions representable as absolutely convergent Laplace-Stieltjes transforms for $t > 0$. The paper gives sufficient conditions for certain solutions of the system $y’ = (R + g(t))y$ to be expressed as Laplace-Stieltjes transforms or as linear combinations of such transforms with coefficients which are powers of $t$.

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