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Pólya's property $ W$ and factorization--A short proof


Author: Robert Ristroph
Journal: Proc. Amer. Math. Soc. 31 (1972), 631-632
MSC: Primary 34.20
DOI: https://doi.org/10.1090/S0002-9939-1972-0288338-5
MathSciNet review: 0288338
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Abstract: For an $ n$th order linear differential expression, the equivalence of Pólya's Property $ {\text{W}}$ and factorization into first order expressions is proven directly and briefly.


References [Enhancements On Off] (What's this?)

  • [1] G. Pólya, On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1922), 312-324. MR 1501228
  • [2] H. W. Turnbull, The theory of determinants, matrices, and invariants, 3rd ed., Dover, New York, 1960, p. 77. MR 24 #A123. MR 0130257 (24:A123)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288338-5
Keywords: Linear differential expression, Wronskian determinant, fundamental set of solutions, Pólya's Property W, factorization of a differential expression
Article copyright: © Copyright 1972 American Mathematical Society

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