Hi. I'm reading a maths paper that discusses positive definite functions and am having difficulty interpreting the notation. Here is the quote:
![{\displaystyle K(x,y)=f(||x-y||),x\in X}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8886f2f5563db8a6773e1ca127766d277818ba89)
where
is again the Euclidean norm on
but
is the unit sphere in
. As there is a simple 1-1 correspondence between
and the standard inner product
for all
, it is more convenient to consider
. Schoenberg proved that, for
, blah blah blah.
OK, three questions:
- Is the "simple 1-1 correspondence" just
?
- What is
?