Proves that the extremal constant C_{d,p} for the sup-norm to L^p-norm inequality on degree-d polynomials on the unit circle satisfies C_{d,p} ≤ dp/2 + 1 for d ≤ 4 (any p ≥ 2) and for p ≥ 6.8 (any d), and conjectures the bound in full generality.
Turán,On rational polynomials, Acta Univ
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Point evaluation for polynomials on the circle
Proves that the extremal constant C_{d,p} for the sup-norm to L^p-norm inequality on degree-d polynomials on the unit circle satisfies C_{d,p} ≤ dp/2 + 1 for d ≤ 4 (any p ≥ 2) and for p ≥ 6.8 (any d), and conjectures the bound in full generality.