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arXiv · 1404.1778

A smooth introduction to the wavefront set

Christian Brouder·Nguyen Viet Dang·Frédéric Hélein
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Abstract

The wavefront set provides a precise description of the singularities of a distribution. Because of its ability to control the product of distributions, the wavefront set was a key element of recent progress in renormalized quantum field theory in curved spacetime, quantum gravity, the discussion of time machines or quantum energy inequalitites. However, the wavefront set is a somewhat subtle concept whose standard definition is not easy to grasp. This paper is a step by step introduction to the wavefront set, with examples and motivation. Many different definitions and new interpretations of the wavefront set are presented. Some of them involve a Radon transform.

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Christian Brouder, Nguyen Viet Dang, Frédéric Hélein. 2014-04-07. A smooth introduction to the wavefront set. https://doi.org/10.1088/1751-8113%2F47%2F44%2F443001

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