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Preprint Number 983
983. Raf Cluckers, Georges Comte, Daniel J. Miller, Jean-Philippe Rolin, Tamara Servi Integration of Oscillatory and Subanalytic Functions E-mail: Submission date: 8 January 2016 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 paper extends the investigation started in [J.-M. Lion, J.-P. Rolin: Volumes, feuilles de Rolle de feuilletages analytiques et théorème de Wilkie Ann. Fac. Sci. Toulouse Math. (6) 7 (1998), no. 1, 93-112] and [R. Cluckers, D. J. Miller: Stability under integration of sums of products of real globally subanalytic functions and their logarithms Duke Math. J. 156 (2011), no. 2, 311-348] to an enriched framework including oscillatory functions. It provides a new example of fruitful interaction between analysis and singularity theory. Mathematics Subject Classification: 26B15, 14P15, 32B20, 42B20, 42A38 (Primary) 03C64, 14P10, 33B10 Keywords and phrases: |
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