Abstract
A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the well-known result for phase functions that are homogeneous of order one.
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Acknowledgments
It is a pleasure to thank Dorothea Bahns for helpful discussions and her detailed comments on the manuscript. I would also like to thank Ingo Witt for valuable comments.
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Work supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Göttingen.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Zahn, J. The wave front set of oscillatory integrals with inhomogeneous phase function. J. Pseudo-Differ. Oper. Appl. 2, 101–113 (2011). https://doi.org/10.1007/s11868-011-0024-7
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DOI: https://doi.org/10.1007/s11868-011-0024-7