Integral means and Pólya factorizations

Author:
Uri Elias

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2071-2075

MSC (1991):
Primary 26A06, 26D10, 34A30

MathSciNet review:
1469404

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Abstract | References | Similar Articles | Additional Information

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.

**[Cop]**W. A. Coppel,*Disconjugacy*, Lecture Notes in Mathematics, Vol. 220, Springer-Verlag, Berlin-New York, 1971. MR**0460785****[Mit]**D. S. Mitrinović,*Analytic inequalities*, Springer-Verlag, New York-Berlin, 1970. In cooperation with P. M. Vasić. Die Grundlehren der mathematischen Wissenschaften, Band 165. MR**0274686****[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]**William F. Trench,*Canonical forms and principal systems for general disconjugate equations*, Trans. Amer. Math. Soc.**189**(1973), 319–327. MR**0330632**, 10.1090/S0002-9947-1974-0330632-X

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Additional Information

**Uri Elias**

Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel

Email:
elias@techunix.technion.ac.il

DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04574-2

Keywords:
Integral means,
P\'{o}lya factorization

Received by editor(s):
January 1, 1997

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1998
American Mathematical Society