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March 2009 Remarks on Krein-Kotani’s correspondence between strings and Herglotz functions
Yuji Kasahara, Shinzo Watanabe
Proc. Japan Acad. Ser. A Math. Sci. 85(3): 22-26 (March 2009). DOI: 10.3792/pjaa.85.22

Abstract

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.

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Yuji Kasahara. Shinzo Watanabe. "Remarks on Krein-Kotani’s correspondence between strings and Herglotz functions." Proc. Japan Acad. Ser. A Math. Sci. 85 (3) 22 - 26, March 2009. https://doi.org/10.3792/pjaa.85.22

Information

Published: March 2009
First available in Project Euclid: 2 March 2009

zbMATH: 1177.47053
MathSciNet: MR2502414
Digital Object Identifier: 10.3792/pjaa.85.22

Subjects:
Primary: 34L05 , 47E05 , 60G51 , 60J55

Keywords: Herglotz function , Krein’s correspondence , Lévy process , spectral measure , Strum-Liouville operator

Rights: Copyright © 2009 The Japan Academy

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Vol.85 • No. 3 • March 2009
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