Remarks on Krein-Kotani’s correspondence between strings and Herglotz functions

Remarks on Krein-Kotani’s correspondence between strings and Herglotz functions

Yuji Kasahara and Shinzo Watanabe

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 85, Number 3 (2009), 22-26.

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

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

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1236004149
Digital Object Identifier: doi:10.3792/pjaa.85.22
Mathematical Reviews number (MathSciNet): MR2502414
Zentralblatt MATH identifier: 1177.47053

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