I would like to know if there are some known results/litterature about the eigenfunctions of the power mean kernel :
which is positive semi-definite for and deiined for .
if not for any , at least for some special cases :
, geometric mean
, harmonic mean
with and standing respectively for and .
For short, eigenfuctions of a kernel are the set of functions such that~:
These eigenfunctions must verify some properties that I won't list here.
For instance has one eigenfunction , since :