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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Explicit conditions for the factorization of $ n$th order linear differential operators


Author: Anton Zettl
Journal: Proc. Amer. Math. Soc. 41 (1973), 137-145
MSC: Primary 34A30
MathSciNet review: 0320413
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Abstract: For any integer $ k$ with $ 1 \leqq k \leqq n$ sufficient conditions on the coefficients $ {p_i}$, are given for the factorization of certain classes of operators $ Ly = {p_n}{y^{(n)}} + {p_{n - 1}}{y^{(n - 1)}} + \cdots + {p_0}y$ into a product $ L = PQ$ where $ P$ and $ Q$ are operators of the same type of orders $ n - k$ and $ k$, respectively. A special case yields that if $ {( - 1)^k}{p_0} \geqq 0$ then $ {y^n} + {p_0}y$ is factorable into a product of two regular differential operators of orders $ n - k$ and $ k$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0320413-X
PII: S 0002-9939(1973)0320413-X
Keywords: Ordinary differential equations, factoring differential operators, Wronskians, property ``W", linear homogeneous differential equations
Article copyright: © Copyright 1973 American Mathematical Society