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Preprint Number 1233

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1233. Raf Cluckers, Immanuel Halupczok, François Loeser and Michel Raibaut
Distributions and wave front sets in the uniform non-archimedean setting

Submission date: 9 June 2017


We study some constructions on distributions in a uniform p-adic context, and also in large positive characteristic, using model theoretic methods. We introduce a class of distributions which we call distributions of C^{exp}-class and which is based on the notion of C^{exp}-class functions from [6]. This class of distributions is stable under Fourier transformation and has various forms of uniform behavior across non-archimedean local fields. We study wave front sets, pull-backs and push-forwards of distributions of this class. In particular we show that the wave front set is always equal to the complement of the zero locus of a C^{exp}-class function. We first revise and generalize some of the results of Heifetz that he developed in the p-adic context by analogy to results about real wave front sets by Hörmander. In the final section, we study sizes of neighborhoods of local constancy of Schwartz-Bruhat functions and their push forwards in relation to discriminants.

Mathematics Subject Classification: Primary 14E18, Secondary 22E50, 03C10, 11S80, 11U09

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Full text arXiv 1706.03003: pdf, ps.

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