Markov inequality for polynomials of degree n with m distinct zeros |
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Authors: | David Benko Tams Erdlyi |
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Institution: | Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA |
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Abstract: | Let
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 for every
. 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
on a finite interval when m c log n. |
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Keywords: | Markov-type inequalities Polynomials with restricted zeros |
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