Park City Lectures on Eigenfunctions, Lecture 5: Lp norms of ...

Recap
So far, for every x ∈ M, we decompose R(λ, x) into dynamical
term on the loop set. It is zero if x is not self-focal point, and it is
the whole integral if it is a self-focal point.
If it is non self-focal, we only get a non-dynamical term ˜R j1 and
another non-dynamical term, R 2 which is small. We show that we
can neglect the points outside of ⋃ M
j=1 B δ(x j ) with δ = λ −1/2 log λ.
We now consider the centers of the balls: i.e. self-focal points.