**ABSTRACT:**

We construct wavelet frames for smooth compact oriented Riemannian manifolds, which are nearly tight (that is, the ratio of the frame bounds can be made as close to 1 as one likes by adjusting the parameters), and for which one has a space-frequency analysis which is analogous to the usual time-frequency analysis on the real line. We also discuss characterizations of function spaces, through knowledge of only the size of frame coefficients.

This is joint work with Azita Mayeli.