Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 7 (2018), 1239-1309.
Integration of oscillatory and subanalytic functions
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.
Duke Math. J., Volume 167, Number 7 (2018), 1239-1309.
Received: 20 July 2016
Revised: 6 November 2017
First available in Project Euclid: 14 March 2018
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 26B15: Integration: length, area, volume [See also 28A75, 51M25]
Secondary: 03C64: Model theory of ordered structures; o-minimality 14P15: Real analytic and semianalytic sets [See also 32B20, 32C05] 32B20: Semi-analytic sets and subanalytic sets [See also 14P15] 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 14P10: Semialgebraic sets and related spaces 33B10: Exponential and trigonometric functions
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
Cluckers, Raf; Comte, Georges; Miller, Daniel J.; Rolin, Jean-Philippe; Servi, Tamara. Integration of oscillatory and subanalytic functions. Duke Math. J. 167 (2018), no. 7, 1239--1309. doi:10.1215/00127094-2017-0056. https://projecteuclid.org/euclid.dmj/1521014410