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NoamL
NoamL
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Let $P$ be a polynomial with real coefficients, and degP=d$\deg P=d$. There is Markov-Berenstein inequality: $P′(x)\leq\frac{d\|P\|}{\sqrt{1-x^2}}$,where $\|P\|=\max_{|x|\le1} |P(x)|$ and $|x|\leq1$. Are there any improvements when $P$ is increasing in the interval $[-1,1]$. I am particularly interested in bounding $|P'(x)|$ around $0$. Any reference would be very much appreciated.

Let $P$ be a polynomial with real coefficients, and degP=d. There is Markov-Berenstein inequality: $P′(x)\leq\frac{d\|P\|}{\sqrt{1-x^2}}$,where $\|P\|=\max_{|x|\le1} |P(x)|$ and $|x|\leq1$. Are there any improvements when $P$ is increasing in the interval $[-1,1]$. I am particularly interested in bounding $|P'(x)|$ around $0$. Any reference would be very much appreciated.

Let $P$ be a polynomial with real coefficients, and $\deg P=d$. There is Markov-Berenstein inequality: $P′(x)\leq\frac{d\|P\|}{\sqrt{1-x^2}}$,where $\|P\|=\max_{|x|\le1} |P(x)|$ and $|x|\leq1$. Are there any improvements when $P$ is increasing in the interval $[-1,1]$. I am particularly interested in bounding $|P'(x)|$ around $0$. Any reference would be very much appreciated.

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NoamL
NoamL
  • 311
  • 1
  • 8

Let $P$ be a polynomial with real coefficients, and degP=d. There is Markov-Berenstein inequality: $P′(x)\leq\frac{d\|P\|}{\sqrt{1-x^2}}$,where $\|P\|=\max_{|x|\le1} |P(x)|$ and $|x|\leq1$. Are there any improvements when $P$ is increasing in the interval $[-1,1]$. I am particularly interested atin bounding $|P'(x)|$ around $0$. Any reference would be very much appreciated.

Let $P$ be a polynomial with real coefficients, and degP=d. There is Markov-Berenstein inequality: $P′(x)\leq\frac{d\|P\|}{\sqrt{1-x^2}}$,where $\|P\|=\max_{|x|\le1} |P(x)|$ and $|x|\leq1$. Are there any improvements when $P$ is increasing in the interval $[-1,1]$. I am particularly interested at bounding $|P'(x)|$ around $0$. Any reference would be very much appreciated.

Let $P$ be a polynomial with real coefficients, and degP=d. There is Markov-Berenstein inequality: $P′(x)\leq\frac{d\|P\|}{\sqrt{1-x^2}}$,where $\|P\|=\max_{|x|\le1} |P(x)|$ and $|x|\leq1$. Are there any improvements when $P$ is increasing in the interval $[-1,1]$. I am particularly interested in bounding $|P'(x)|$ around $0$. Any reference would be very much appreciated.

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NoamL
NoamL
  • 311
  • 1
  • 8

Markov-Bernstein like inequalities for monotone polynomials

Let $P$ be a polynomial with real coefficients, and degP=d. There is Markov-Berenstein inequality: $P′(x)\leq\frac{d\|P\|}{\sqrt{1-x^2}}$,where $\|P\|=\max_{|x|\le1} |P(x)|$ and $|x|\leq1$. Are there any improvements when $P$ is increasing in the interval $[-1,1]$. I am particularly interested at bounding $|P'(x)|$ around $0$. Any reference would be very much appreciated.