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
Jean Favard (28 August 190221 January 1965) was a French mathematician who worked on analysis.
Favard was born in Peyrat-la-Nonière. During World War II he was a prisoner of war in Germany.
He also was a President of the French Mathematical ...
, and after the Soviet mathematicians
Naum Akhiezer
Naum Ilyich Akhiezer ( uk, Нау́м Іллі́ч Ахіє́зер; russian: link=no, Нау́м Ильи́ч Ахие́зер; 6 March 1901 – 3 June 1980) was a Soviet and Ukrainian mathematician of Jewish origin, known for his works in appr ...
and
Mark Krein
Mark Grigorievich Krein ( uk, Марко́ Григо́рович Крейн, russian: Марк Григо́рьевич Крейн; 3 April 1907 – 17 October 1989) was a Soviet mathematician, one of the major figures of the Soviet school of fu ...
.
Particular values
:
:
Uses
This constant is used in solutions of several extremal problems, for example
* Favard's constant is the sharp constant in
Jackson's inequality In approximation theory, Jackson's inequality is an inequality bounding the value of function's best approximation by polynomials, algebraic or trigonometric polynomials in terms of the modulus of continuity or modulus of smoothness of the function ...
for
trigonometric polynomial In the mathematical subfields of numerical analysis and mathematical analysis, a trigonometric polynomial is a finite linear combination of functions sin(''nx'') and cos(''nx'') with ''n'' taking on the values of one or more natural numbers. The c ...
s
* the sharp constants in the
Landau–Kolmogorov inequality In mathematics, the Landau–Kolmogorov inequality, named after Edmund Landau and Andrey Kolmogorov, is the following family of interpolation inequalities between different derivatives of a function ''f'' defined on a subset ''T'' of the real ...
are expressed via Favard's constants
* Norms of periodic
perfect splines.
References
*
Mathematical constants
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