Measures essentially of finite type and spectral asymptotics of fractal laplacians

Useful measure-theoretic properties can be extracted from measures that are said to be essentially of finite type (EFT), making it possible to study the analytic properties of the Laplacians associated with the measure. In this chapter, we explain how EFT leads to the spectral asymptotics of fractal Laplacians associated with self-similar measures defined by one-dimensional iterated function systems with overlaps. We then discuss some applications to heat kernel estimates, the wave propagation speed problem, spectral asymptotics of Schrödinger operators and computing L^q-spectrum.