INTEGRATION OF OSCILLATORY AND SUBANALYTIC FUNCTIONS

Raf Cluckers (1, 2) , Georges Comte (3, 4) , Daniel J Miller (5) , Jean-Philippe Rolin (6, 7) , Tamara Servi (8)

1 Université de Lille
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
4 LAMA - Laboratoire de Mathématiques
5 Emporia State University
6 UB - Université de Bourgogne
7 IMB - Institut de Mathématiques de Bourgogne [Dijon]
8 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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 paper extends the investigation started in [26] and [8] to an enriched framework including oscillatory functions. It provides a new example of fruitful interaction between analysis and singularity theory.

Domaines: Mathématiques [math]

Raf Cluckers, Georges Comte, Daniel J Miller, Jean-Philippe Rolin, Tamara Servi. INTEGRATION OF OSCILLATORY AND SUBANALYTIC FUNCTIONS. Duke Mathematical Journal, 2018, ⟨10.1215/00127094-2017-0056⟩. ⟨hal-03798616⟩