What is recorded here?
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.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
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.
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People and systems
Eugène Remes
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.
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English catalogue narrative
Remez sharp polynomial bound from control on a subset of prescribed measure
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
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.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Eugène Remes
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.