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A stationary phase type estimate


Authors: T. Alazard, N. Burq and C. Zuily
Journal: Proc. Amer. Math. Soc. 145 (2017), 2871-2880
MSC (2010): Primary 35A23, 42B20, 35C15
DOI: https://doi.org/10.1090/proc/13199
Published electronically: February 23, 2017
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Abstract: The purpose of this note is to prove a stationary phase estimate well adapted to parameter dependent phases. In particular, no discussion is made on the positions (and behavior) of critical points, no lower or upper bound on the gradient of the phase is assumed, and the dependence of the constants with respect to derivatives of the phase and symbols is explicit.


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Additional Information

T. Alazard
Affiliation: Département de Mathématiques, UMR 8553 du CNRS, Ecole Normale Supérieure, 45, rue d’Ulm 75005 Paris Cedex, France

N. Burq
Affiliation: Laboratoire de Mathématiques d’Orsay, UMR 8628 du CNRS, Université Paris-Sud, 91405 Orsay Cedex, France

C. Zuily
Affiliation: Laboratoire de Mathématiques d’Orsay, UMR 8628 du CNRS, Université Paris-Sud, 91405 Orsay Cedex, France

DOI: https://doi.org/10.1090/proc/13199
Received by editor(s): January 8, 2016
Received by editor(s) in revised form: February 12, 2016, March 7, 2016, and March 14, 2016
Published electronically: February 23, 2017
Additional Notes: The authors were supported in part by Agence Nationale de la Recherche project ANAÉ ANR-13-BS01-0010-03. The second author was supported in part by Agence Nationale de la Recherche project NOSEVOL, 2011 BS01019 01.
Communicated by: Michael Hitrik
Article copyright: © Copyright 2016 American Mathematical Society