Constructive function theory
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In mathematical analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is closely related to approximation theory. The term was coined by Sergei Bernstein.
In mathematical analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is closely related to approximation theory. The term was coined by Sergei Bernstein. ==Example== Let f be a 2π-periodic function. Then f is α-Hölder for some 0 n of degree n such that \max_{0 \leq x \leq 2\pi} | f(x) - P_n(x) | \leq \frac{C(f)}{n^\alpha}, where C(f) is a positive number depending on f. The "only if" is due to Dunham Jackson, see Jackson's inequality; the "if" part is due to Sergei Bernstein, see Bernstein's theorem (approximation theory). ==Notes== ==References==
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