On functions K and E generated by a sequence of moments

Avner Kiro, Mikhail Sodin

Research output: Contribution to journalArticlepeer-review

Abstract

For a class of functions γ analytic in the angle {s:|arg(s)|<α0} with π2<α0<π, we describe the asymptotic behaviour of the entire function E(z)=∑n≥0znγ(n+1)and of the analytic function K(z)=12πi∫c−i∞c+i∞z−sγ(s)dsthat solves the moment problem ∫0tnK(t)dt=γ(n+1),n≥0.

Original languageEnglish
Pages (from-to)443-477
Number of pages35
JournalExpositiones Mathematicae
Volume35
Issue number4
DOIs
StatePublished - Dec 2017

Keywords

  • Asymptotics
  • Entire functions represented by Taylor series
  • Saddle point method
  • The Mellin transform

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