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

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

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.

scholarly journals Wave Front Sets with respect to the Iterates of an Operator with Constant Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
C. Boiti ◽  
D. Jornet ◽  
J. Juan-Huguet
Keyword(s):  
Differential Operator ◽  
Wave Front ◽  
Partial Differential Operator ◽  
Regularity Theorem ◽  
Wave Front Set ◽  
Open Set ◽  
Wave Front Sets ◽  
Constant Coefficients ◽  
New Type ◽  
Classical Distribution

We introduce the wave front setWF*P(u)with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distributionu∈𝒟′(Ω)in an open set Ω in the setting of ultradifferentiable classes of Braun, Meise, and Taylor. We state a version of the microlocal regularity theorem of Hörmander for this new type of wave front set and give some examples and applications of the former result.

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