scholarly journals Distributions and wave front sets in the uniform non‐archimedean setting

2018 ◽  
Vol 5 (1) ◽  
pp. 97-131 ◽  
Author(s):  
Raf Cluckers ◽  
Immanuel Halupczok ◽  
François Loeser ◽  
Michel Raibaut
Keyword(s):  
Wave Front ◽  
Wave Front Sets

scholarly journals Characterization of Wave Front Sets in Fourier-Lebesgue Spaces and Its Application

2013 ◽  
Vol 56 (1) ◽  
pp. 1-17
Author(s):  
Keiichi Kato ◽  
Masaharu Kobayashi ◽  
Shingo Ito
Keyword(s):  
Wave Front ◽  
Lebesgue Spaces ◽  
Wave Front Sets

scholarly journals Wave front sets and the viscosity method

1973 ◽  
Vol 79 (2) ◽  
pp. 431-437 ◽  
Author(s):  
Joel A. Smoller ◽  
Michael E. Taylor
Keyword(s):  
Wave Front ◽  
Viscosity Method ◽  
Wave Front Sets

A Note on Wave-front Sets of Roumieu Type Ultradistributions

2013 ◽  
pp. 239-252
Author(s):  
Karoline Johansson ◽  
Stevan Pilipović ◽  
Nenad Teofanov ◽  
Joachim Toft
Keyword(s):  
Wave Front ◽  
Wave Front Sets

Motivic Wave Front Sets

2019 ◽  
Author(s):  
Michel Raibaut
Keyword(s):  
Tensor Product ◽  
Wave Front ◽  
Lie Groups ◽  
Wave Front Set ◽  
Singular Support ◽  
Valued Field ◽  
Wave Front Sets ◽  
Multiplicative Subgroups ◽  
Products Of Distributions ◽  
Lambda Wave

Abstract The concept of wave front set was introduced in 1969–1970 by Sato in the hyperfunctions context [1, 34] and by Hörmander [23] in the $\mathcal C^{\infty }$ context. Howe in [25] used the theory of wave front sets in the study of Lie groups representations. Heifetz in [22] defined a notion of wave front set for distributions in the $p$-adic setting and used it to study some representations of $p$-adic Lie groups. In this article, we work in the $k\mathopen{(\!(} t \mathopen{)\!)}$-setting with $k$ a Characteristic 0 field. In that setting, balls are no longer compact but working in a definable context provides good substitutes for finiteness and compactness properties. We develop a notion of definable distributions in the framework of [13] and [14] for which we define notions of singular support and $\Lambda$-wave front sets (relative to some multiplicative subgroups $\Lambda$ of the valued field) and we investigate their behavior under natural operations like pullback, tensor product, and products of distributions.

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