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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A class of Nevanlinna functions related to singular Sturm-Liouville problems
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by Seppo Hassi, Manfred Möller and Henk de Snoo PDF
Proc. Amer. Math. Soc. 134 (2006), 2885-2893 Request permission

Abstract:

The class of Nevanlinna functions consists of functions which are holomorphic off the real axis, which are symmetric with respect to the real axis, and whose imaginary part is nonnegative in the upper halfplane. The Kac subclass of Nevanlinna functions is defined by an integrability condition on the imaginary part. In this note a further subclass of these Kac functions is introduced. It involves an integrability condition on the modulus of the Nevanlinna functions (instead of the imaginary part). The characteristic properties of this class are investigated. The definition of the new class is motivated by the fact that the Titchmarsh-Weyl coefficients of various classes of Sturm-Liouville problems (under mild conditions on the coefficients) actually belong to this class.
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Additional Information
  • Seppo Hassi
  • Affiliation: Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland
  • Email: sha@uwasa.fi
  • Manfred Möller
  • Affiliation: Department of Mathematics, University of the Witwatersrand, Wits, 2050, South Africa
  • MR Author ID: 212175
  • Email: manfred@maths.wits.ac.za
  • Henk de Snoo
  • Affiliation: Department of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV Groningen, Nederland
  • Email: desnoo@math.rug.nl
  • Received by editor(s): August 3, 2004
  • Received by editor(s) in revised form: April 12, 2005
  • Published electronically: April 7, 2006
  • Additional Notes: The authors gratefully acknowledge the support of the NRF of South Africa under GUN 2053746, of the Research Institute for Technology of the University of Vaasa, and of the Dutch Association for Mathematical Physics under MF04/62a.
  • Communicated by: Joseph A. Ball
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 2885-2893
  • MSC (2000): Primary 30D15; Secondary 34B20
  • DOI: https://doi.org/10.1090/S0002-9939-06-08295-5
  • MathSciNet review: 2231612