Μ operator

From formulasearchengine
Jump to navigation Jump to search

In mathematics, the Fejér kernel is used to express the effect of Cesàro summation on Fourier series. It is a non-negative kernel, giving rise to an approximate identity.

Plot of several Fejér kernels

The Fejér kernel is defined as

where

is the kth order Dirichlet kernel. It can also be written in a closed form as

,

where this expression is defined.[1] It is named after the Hungarian mathematician Lipót Fejér (1880–1959).

The important property of the Fejér kernel is with average value of . The convolution Fn is positive: for of period it satisfies

and, by Young's inequality,

for every

for continuous function ; moreover,

for every ()

for continuous function . Indeed, if is continuous, then the convergence is uniform.

See also

References

  1. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534