Special functions, integral equations and a Riemann-Hilbert problem

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

4 Scopus Citations
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Author(s)

  • R. Wong
  • Yu-Qiu Zhao

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)4367-4380
Journal / PublicationProceedings of the American Mathematical Society
Volume144
Issue number10
Online published3 Jun 2016
Publication statusPublished - Oct 2016

Abstract

We consider a pair of special functions, uβ and vβ, defined respectively as the solutions to the integral equations [Formula presented] where (Formula presented) for β ∈ (0, 1). In this note, we establish the existence and uniqueness of uβ and vβ which are bounded and continuous in [0,+∞). Also, we show that a solution to a model Riemann-Hilbert problem in Kriecherbauer and McLaughlin [Int. Math. Res. Not., 1999] can be constructed explicitly in terms of these functions. A preliminary asymptotic study is carried out on the Stokes phenomena of these functions by making use of their connection formulas. Several open questions are also proposed for a thorough investigation of the analytic and asymptotic properties of the functions uβ and vβ, and a related new special function Gβ.

Research Area(s)

  • Asymptotics, Freud weight, Integral equation, Riemann-Hilbert problem, Special function, Stokes phenomenon

Citation Format(s)

Special functions, integral equations and a Riemann-Hilbert problem. / Wong, R.; Zhao, Yu-Qiu.
In: Proceedings of the American Mathematical Society, Vol. 144, No. 10, 10.2016, p. 4367-4380.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review