Difference between revisions of "Fejér singular integral"
From Encyclopedia of Mathematics
Ulf Rehmann (talk | contribs) m (moved Fejér singular integral to Fejer singular integral: ascii title) |
(TeX) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
| + | {{TEX|done}} | ||
An integral of the form | An integral of the form | ||
| − | + | $$\sigma_n(f,x)=\frac1\pi\int\limits_{-\pi}^\pi f(x+t)\Phi_n(t)dt,$$ | |
where | where | ||
| − | + | $$\Phi_n(t)=\frac{1}{2(n+1)}\frac{\sin^2(n+1)t/2}{\sin^2t/2}$$ | |
| − | is the Fejér kernel. The Fejér singular integral is an integral representation of the Fejér sums (cf. [[Fejér sum|Fejér sum]]) | + | is the Fejér kernel. The Fejér singular integral is an integral representation of the Fejér sums (cf. [[Fejér sum|Fejér sum]]) $\sigma_n(f,x)$. |
For references see [[Fejér sum|Fejér sum]]. | For references see [[Fejér sum|Fejér sum]]. | ||
Latest revision as of 14:13, 31 July 2014
An integral of the form
$$\sigma_n(f,x)=\frac1\pi\int\limits_{-\pi}^\pi f(x+t)\Phi_n(t)dt,$$
where
$$\Phi_n(t)=\frac{1}{2(n+1)}\frac{\sin^2(n+1)t/2}{\sin^2t/2}$$
is the Fejér kernel. The Fejér singular integral is an integral representation of the Fejér sums (cf. Fejér sum) $\sigma_n(f,x)$.
For references see Fejér sum.
How to Cite This Entry:
Fejér singular integral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fej%C3%A9r_singular_integral&oldid=22409
Fejér singular integral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fej%C3%A9r_singular_integral&oldid=22409
This article was adapted from an original article by S.A. Telyakovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article