Effective estimation of some oscillatory integrals related to infinitely divisible distributions

We present a practical framework to prove, in a simple way, two-term asymptotic expansions for Fourier integrals I ( t ) = ∫ R ( e i t ϕ ( x ) - 1 ) d μ ( x ) , where  μ is a probability measure on  R and  ϕ is measurable. This applies to many basic cases, in link with Levy’s continuity theorem. We...

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Veröffentlicht in:	The Ramanujan journal 2022-02, Vol.57 (2), p.849-861
Hauptverfasser:	Bettin, S., Drappeau, S.
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic series Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Integrals Mathematics Mathematics and Statistics Number Theory
Online-Zugang:	Volltext
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