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Proceedings of the American Mathematical Society
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An extremal property of Jacobi polynomials in two-sided Chernoff-type inequalities for higher order derivatives


Author: Vladimir D. Stepanov
Journal: Proc. Amer. Math. Soc. 136 (2008), 1589-1597
MSC (2000): Primary 26D10; Secondary 33C45, 60E15
Published electronically: January 4, 2008
MathSciNet review: 2373588
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Abstract | References | Similar Articles | Additional Information

Abstract: For a weight function generating the classical Jacobi polynomials, the sharp double estimate of the distance from the subspace of all polynomials of an arbitrary fixed order is established.


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  • 1. Herman Chernoff, A note on an inequality involving the normal distribution, Ann. Probab. 9 (1981), no. 3, 533–535. MR 614640 (82f:60050)
  • 2. Herm Jan Brascamp and Elliott H. Lieb, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Functional Analysis 22 (1976), no. 4, 366–389. MR 0450480 (56 #8774)
  • 3. W. Bischoff and M. Fichter, Optimal lower and upper bounds for the 𝐿_{𝑝}-mean deviation of functions of a random variable, Math. Methods Statist. 9 (2000), no. 3, 237–269. MR 1807094 (2001k:60022)
  • 4. V. D. Stepanov, An extremal property of Chebyshev polynomials, Tr. Mat. Inst. Steklova 248 (2005), no. Issled. po Teor. Funkts. i Differ. Uravn., 237–249 (Russian, with Russian summary); English transl., Proc. Steklov Inst. Math. 1 (248) (2005), 230–242. MR 2165931 (2006h:41006)
  • 5. P. K. Suetin, Klassicheskie ortogonalnye mnogochleny, “Nauka”, Moscow, 1979 (Russian). Second edition, augmented. MR 548727 (80h:33001)
  • 6. G. Aleksič, Problemy skhodimosti ortogonalnykh ryadov, Translated from the English by A. V. Efimov. Translation edited by P. L. Ul′janov, Izdat. Inostran. Lit., Moscow, 1963 (Russian). MR 0218828 (36 #1912)

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Additional Information

Vladimir D. Stepanov
Affiliation: People Friendship University, Miklukho-Maklai 6, Moscow, 117198, Russia
Email: vstepanov@sci.pfu.edu.ru

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09218-6
PII: S 0002-9939(08)09218-6
Keywords: Jacobi polynomials, Chernoff inequality
Received by editor(s): March 4, 2006
Published electronically: January 4, 2008
Additional Notes: The work of the author was financially supported by the Russian Foundation for Basic Researches (Projects 05–01–00422, 06–01–00341, 06–01–04006 and 07–01–00054) and by the INTAS grant 05-1000008-8157.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.