Favard constant
Encyclopedia
In mathematics
, the Favard constant, also called the Akhiezer–Krein–Favard constant, of order r is defined as
This constant is named after the French mathematician Jean Favard
, and after the Soviet mathematicians Naum Akhiezer and Mark Krein.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the Favard constant, also called the Akhiezer–Krein–Favard constant, of order r is defined as
This constant is named after the French mathematician Jean Favard
Jean Favard
Jean Favard was a French mathematician who worked on analysis.During World War II he was a prisoner of war in Germany.He also was a President of the French Mathematical Society in 1946....
, and after the Soviet mathematicians Naum Akhiezer and Mark Krein.
Uses
This constant is used in solutions of several extremal problems, for example- Favard's constant is the sharp constant in Jackson's inequalityJackson's inequalityIn approximation theory, Jackson's inequality is an inequality bounding the value of function's best approximation by algebraic or trigonometric polynomials in terms of the modulus of continuity of its derivatives...
for trigonometric polynomials - the sharp constants in the Landau–Kolmogorov inequality are expressed via Favard's constants.
- Norm of Euler spline