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

Perron-Frobenius operator
Following Safarov, at a self-focal point x define
U x : L 2 (Sx ∗ M, dµ x ) → L 2 (Sx ∗ M, dµ x ), U x f (ξ) := f (Φ x (ξ)) √ J x (ξ).
(13)
Here, J x is the Jacobian of the map Φ x , i.e. Φ ∗ x|dξ| = J x (ξ)|dξ|.
Also define
U x ± (λ) = e iλT ± x
U x ± . (14)