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Proceedings of the American Mathematical Society

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Finite moments perturbations of $ y''=0$ in Banach algebras

Authors: Renato Spigler and Marco Vianello
Journal: Proc. Amer. Math. Soc. 119 (1993), 97-103
MSC: Primary 34G10; Secondary 34E05
MathSciNet review: 1181175
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Abstract: Rigorous asymptotics for a basis of $ y'' + g(x)y = 0,\;x \in [1, + \infty )$, is derived in the framework of Banach algebras. The key assumption is $ \int_1^{ + \infty } {{x^k}} \vert\vert g(x)\vert\vert dx < \infty $ for $ k = 1$ or $ k = 2$. Such results improve and generalize previous work on linear second-order matrix differential equations.

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Keywords: Abstract linear differential equations, matrix differential equations, Banach algebras, asymptotic representations
Article copyright: © Copyright 1993 American Mathematical Society

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