Mathematics Seminar
Date: Monday, 14 October 2024
Time: 10.30 - 11.30 AM
Venue: Seminar Hall
Tightly relating L_1 and L_{\infty} norms of polynomials over reals
Vipul Arora
National University of Singapore.
14-10-24

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Abstract

We present a new result, that gives tight upper, and lower bounds for the L_{\infty} norm of an individual degree-d, n-variate polynomial with real coefficients, over the solid cube [-1,1]^n, in terms of its L_1 norm, over the same solid cube.

The techniques used are elementary real analysis, Legendre polynomials, and a lesser known inequality about polynomials and their derivatives, proven by the (even lesser known) brother of the famous Andrey Markov, Vladimir Markov.The techniques used are elementary real analysis, Legendre polynomials, and a lesser known inequality about polynomials and their derivatives, proven by the (even lesser known) brother of the famous Andrey Markov, Vladimir Markov.