Fejér's theorem [SEP] named after
Fejér's theorem
In mathematics, Fejér's theorem, named for Hungarian mathematician Lipót Fejér, states that if "f":R → C is a continuous function with period 2π, then the sequence (σ) of Cesàro means of the sequence ("s") of partial sums of the Fourier series of "f" converges uniformly to "f" on [-π,π].
Explicitly,
where
and
with "F" being the "n"th order Fejér kernel.
A more general
coefficients have to be zero
- Bramble–Hilbert lemma — upper bound on L error of polynomial approximation in multiple dimensions
- Discrete Chebyshev polynomials — polynomials orthogonal with respect to a discrete measure
- Favard's theorem — polynomials satisfying suitable 3-term recurrence relations are orthogonal polynomials
- Approximation by Fourier series / trigonometric polynomials:
- Jackson's inequality — upper bound for best approximation by a trigonometric polynomial
- Bernstein's theorem (approximation theory) — a converse to Jackson's inequality
- Fejér's theorem — Cesàro