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Integral means and Pólya factorizations

Author(s): Uri Elias
Journal: Proc. Amer. Math. Soc. 126 (1998), 2071-2075.
MSC (1991): Primary 26A06, 26D10, 34A30
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Abstract: Integral means of functions and their derivatives are studied. We find a relation between integral means and the Pólya factorization of ordinary linear differential operators.

References:

[Cop]: Coppel, W. A., Disconjugacy, Lecture Notes in Math., vol. 200, Springer Verlag, Berlin, 1971. MR 57:778
[Mit]: Mitrinovic, D. S., Analytic inequalities, Springer Verlag, Berlin, 1970. MR 43:448
[Pol]: Pólya, G., On the mean value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1924), 312-324.
[Tre]: Trench, W. F., Canonical forms and principal systems for general disconjugate equations, Trans. Amer. Math. Soc. 189 (1974), 319-327. MR 48:8969


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