Journal of the
Korean Mathematical Society JKMS

One-dimensional diffusion processes are characterized by Feller's data of canonical scales and speed measures and, if we apply the theory of spectral functions of strings developed by M. G. Krein, Feller's data are determined by paris of spectral characteristic functions so that theses pairs may be considered as invariants of diffusions under the homeomorphic change of state spaces. We show by examples how these invariants are useful in the study of onedimensional diffusion processes.

Keywords: one-dimensional diffusion process, spectral characteristic function of strings, Krein's correspondence

MSC numbers: 60J60