Gevrey asymptotics and Stieltjes transforms of algebraically decaying functions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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  • R. Wong
  • Yu-Qiu Zhao

Related Research Unit(s)


Original languageEnglish
Pages (from-to)625-644
Journal / PublicationProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2019
Publication statusPublished - 8 Mar 2002


The development of asymptotic expansions of Stieltjes transforms of exponentially decaying functions has been well established. In this paper, we are concerned with the more difficult case in which the functions decay only algebraically at infinity. By using a Gevrey-type condition, we obtain an exponentially improved asymptotic expansion, and give three representation theorems to show that the Stieltjes transform of algebraically decaying functions can be written as the difference of two integral transforms with exponentially decaying kernels, thus making the asymptotic theory developed for integral transforms with exponentially decaying kernels relevant to Stieltjes transforms of algebraically decaying functions, including the smoothing of the Stokes phenomenon.

Research Area(s)

  • Gevrey asymptotics, Stieltjes transforms, Stokes phenomenon