Markov inequality for polynomials of degree n with m distinct zeros
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Let Pnm be the collection of all polynomials of degree at most n with real coefficients that have at most m distinct complex zeros. We prove that A figure is presented. For every P∈ Pnm. This is far away from what we expect. We conjecture that the Markov factor 32.8mn above may be replaced by cmn with an absolute constant c > 0. We are not able to prove this conjecture at the moment. However, we think that our result above gives the best-known Markov-type inequality for Pnm on a finite interval when m ≤ c log n. © 2003 Elsevier Science (USA). All rights reserved.
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