SWhat changed
For a real polynomial p of degree at most n, bounded by k on a measurable subset E of an interval S of length l with measure at least lambda=theta*l, 0<theta<1, the interval supremum is at most k*T_n(2/theta-1). Shifted Chebyshev polynomials on an endpoint interval of length lambda attain the bound.
Scientific scope
For a real polynomial p of degree at most n, bounded by k on a measurable subset E of an interval S of length l with measure at least lambda=theta*l, 0<theta<1, the interval supremum is at most k*T_n(2/theta-1). Shifted Chebyshev polynomials on an endpoint interval of length lambda attain the bound. One-dimensional real polynomial and Lebesgue-measure control, not a general measurable-function, multivariate or arbitrary-set inequality with the same constant. Degree n>=1 and k>0; n=0 is trivial and not included in an extremizer-uniqueness claim. The source's footnote links earlier approximation algorithms, which are not separately claimed as established by this inequality paper. One-dimensional Lebesgue-measure statement, not arbitrary functions or unchanged multivariate constants. Positive k,0<theta<1; constant-polynomial case does not inherit a uniqueness-of-extremizer assertion. Kiev byline retained without present-day-country guess.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. One-dimensional real polynomial and Lebesgue-measure control, not a general measurable-function, multivariate or arbitrary-set inequality with the same constant. Degree n>=1 and k>0; n=0 is trivial and not included in an extremizer-uniqueness claim. The source's footnote links earlier approximation algorithms, which are not separately claimed as established by this inequality paper. One-dimensional Lebesgue-measure statement, not arbitrary functions or unchanged multivariate constants. Positive k,0<theta<1; constant-polynomial case does not inherit a uniqueness-of-extremizer assertion. Kiev byline retained without present-day-country guess.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.5. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
Full scientific record · Browse contribution grades · Request a correction