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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a polynomial inequality
of Kolmogoroff's type


Authors: B. D. Bojanov and A. K. Varma
Journal: Proc. Amer. Math. Soc. 124 (1996), 491-496
MSC (1991): Primary 41A17
MathSciNet review: 1291763
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove an inequality of the form

\begin{displaymath}\|f^{(j)}\|^2\leq A\|f^{(m)}\|^2+B\|f\|^2\end{displaymath}

for polynomials of degree $n$ and any fixed $0<j<m\leq n$. Here $\|\cdot\|$ is the $L_2$-norm on $(-\infty,\infty)$ with a weight $e^{-t^2}$. The coefficients $A$ and $B$ are given explicitly and depend on $j,m$ and $n$ only. The equality is attained for the Hermite orthogonal polynomials $H_n(t)$.


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Additional Information

B. D. Bojanov
Affiliation: Department of Mathematics, University of Sofia, Blvd. James Boucher 5, 1126 Sofia, Bulgaria
Email: BOR@BGEARN.bitnet

A. K. Varma
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03024-9
PII: S 0002-9939(96)03024-9
Received by editor(s): January 3, 1994
Received by editor(s) in revised form: August 25, 1994
Additional Notes: The first author was supported in part by the Bulgarian Ministry of Science under Grant No. MM-414
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society



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