Proc. Japan Acad. Ser. A Math. Sci. 85 (3), 22-26, (March 2009) DOI: 10.3792/pjaa.85.22
Yuji Kasahara, Shinzo Watanabe
KEYWORDS: Strum-Liouville operator, spectral measure, Krein’s correspondence, Herglotz function, Lévy process, 47E05, 34L05, 60J55, 60G51
In the study of spectral functions of Strum-Liouville operators, S. Kotani found a one-to-one correspondence between the operators and Herglotz functions determining the spectral measures. In the present paper we give another correspondence to a class of Lévy processes obtained as a compensated integrals of Brownian local times. As an application the continuity theorem of Kotani’s correspondence is extended.