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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: 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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Additional Information

Vladimir D. Stepanov
Affiliation: People Friendship University, Miklukho-Maklai 6, Moscow, 117198, Russia

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.