Title :

Integration of oscillatory and subanalytic functions

Author(s) :

Cluckers, Raf [Auteur correspondant]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Comte, Georges [Auteur]
Laboratoire de Mathématiques [LAMA]
Miller, Daniel [Auteur]
Rolin, Jean-Philippe [Auteur]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Servi, Tamara [Auteur]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]

Journal title :

Duke Mathematical Journal

Pages :

1239-1309

Publisher :

Duke University Press

Publication date :

2018-05

ISSN :

0012-7094

English keyword(s) :

Stability under integration
Oscillatory integrals
Fourier transforms
Globally subanalytic functions
Constructible functions
Preparation theorems
Uniformly distributed functions
Oscillation index
Families of exponential periods
o-minimality

HAL domain(s) :

Mathématiques [math]/Géométrie algébrique [math.AG]

English abstract : [en]

We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials. This article extends the investigation ...
Show more >We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials. This article extends the investigation started by Lion and Rolin and Cluckers and Miller to an enriched framework including oscillatory functions. It provides a new example of fruitful interaction between analysis and singularity theory.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Définissabilité en géométrie non archimédienne
Singularités de Trajectoires de Champs de Vecteurs Analytiques et Algébriques

Comment :

Final version. Accepted for publication in Duke Math. Journal. Changes in proofs: from Section 6 to the end, we now use the theory of continuously uniformly distributed modulo 1 functions that provides a uniform technical point of view in the proofs of limit statements

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL