On a Polynomial Inequality of Kolmogoroff’s Type

  title={On a Polynomial Inequality of Kolmogoroff’s Type},
  author={Borislav Bojanov and Ashok K. Varma},
We prove an inequality of the form ‖f‖ ≤ A‖f‖ +B‖f‖ for polynomials of degree n and any fixed 0 < j < m ≤ n. Here ‖ · ‖ is the L2-norm on (−∞,∞) 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 Hn(t). 


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