On functions K and E generated by a sequence of moments

Avner Kiro; Mikhail Sodin

doi:10.1016/j.exmath.2017.05.004

On functions K and E generated by a sequence of moments

Avner Kiro, Mikhail Sodin

Tel Aviv University

Research output: Contribution to journal › Article › peer-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 ∫₀^∞tⁿK(t)dt=γ(n+1),n≥0.

Original language	English
Pages (from-to)	443-477
Number of pages	35
Journal	Expositiones Mathematicae
Volume	35
Issue number	4
DOIs	https://doi.org/10.1016/j.exmath.2017.05.004
State	Published - Dec 2017

Keywords

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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.exmath.2017.05.004

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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 ∫0∞tnK(t)dt=γ(n+1),n≥0.",

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AU - Sodin, Mikhail

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AB - 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 ∫0∞tnK(t)dt=γ(n+1),n≥0.

KW - Asymptotics

KW - Entire functions represented by Taylor series

KW - Saddle point method

KW - The Mellin transform

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DO - 10.1016/j.exmath.2017.05.004

M3 - مقالة

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VL - 35

SP - 443

EP - 477

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 4

ER -

On functions K and E generated by a sequence of moments

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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