Landau kernel

For k the Landau kernel Lk(t) is defined as

Lk={1ck(1-t2)kif t[-1,1]0otherwise



Lk is nonnegative and continuousMathworldPlanetmath on . Due to the choice of ck we have


Also we have for all positive, real r:

\[-r,r]Lk(t)𝑑t 2ckr1(1-t2)k𝑑t

Therefore (Lk)k is a Dirac sequence.

Title Landau kernel
Canonical name LandauKernel
Date of creation 2013-03-22 14:11:38
Last modified on 2013-03-22 14:11:38
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 7
Author mathwizard (128)
Entry type Definition
Classification msc 26A30