Integration of oscillatory and subanalytic functions

Abstract : 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.
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Submitted on : Saturday, October 20, 2018 - 6:46:19 PM
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Raf Cluckers, Georges Comte, Daniel Miller, Jean-Philippe Rolin, Tamara Servi. Integration of oscillatory and subanalytic functions. Duke Mathematical Journal, Duke University Press, 2018, 167 (7), pp.1239-1309. ⟨10.1215/00127094-2017-0056⟩. ⟨hal-01900046⟩



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