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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Stieltjes functions of finite order and hyperbolic monotonicity
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by Lennart Bondesson and Thomas Simon PDF
Trans. Amer. Math. Soc. 370 (2018), 4201-4222 Request permission


A class of Stieltjes functions of finite type is introduced. These satisfy Widder’s conditions on the successive derivatives up to some finite order and are not necessarily smooth. We show that such functions have a unique integral representation along some generic kernel which is a truncated Laurent series approximating the standard Stieltjes kernel. We then obtain a two-to-one correspondence, via the logarithmic derivative, between these functions and a subclass of hyperbolically monotone functions of finite type. This correspondence generalizes a representation of HCM functions in terms of two Stieltjes transforms earlier obtained by the first author.
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Additional Information
  • Lennart Bondesson
  • Affiliation: Department of Mathematics and Mathematical Statistics, Umeå  University, 90183 Umeå, Sweden
  • MR Author ID: 39130
  • Email:
  • Thomas Simon
  • Affiliation: Laboratoire Paul Painlevé, Université de Lille 1, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France
  • MR Author ID: 640288
  • Email:
  • Received by editor(s): April 19, 2016
  • Received by editor(s) in revised form: November 7, 2016
  • Published electronically: February 14, 2018
  • Additional Notes: The second author would like to thank Jean-François Burnol for several discussions related to this paper.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 4201-4222
  • MSC (2010): Primary 44A15; Secondary 60E05, 60E10
  • DOI:
  • MathSciNet review: 3811525