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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Integration of ordinary linear differential equations by Laplace-Stieltjes transforms


Authors: James D’Archangelo and Philip Hartman
Journal: Trans. Amer. Math. Soc. 204 (1975), 245-266
MSC: Primary 34A25
DOI: https://doi.org/10.1090/S0002-9947-1975-0357935-8
MathSciNet review: 0357935
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0357935-8
Keywords: Laplace-Stieltjes transform, linear differential equations, Bessel and Legendre functions
Article copyright: © Copyright 1975 American Mathematical Society