scholarly journals Characterization of wave front sets by wavelet transforms

2006 ◽  
Vol 58 (3) ◽  
pp. 369-391 ◽  
Author(s):  
Stevan Pilipović ◽  
Mirjana Vuletić
Keyword(s):  
Wave Front ◽  
Wavelet Transforms ◽  
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 On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets

2006 ◽  
Vol 133 (31) ◽  
pp. 115-136 ◽  
Author(s):  
Claudia Garetto ◽  
G. Hormann
Keyword(s):  
Wave Front ◽  
Pseudodifferential Operators ◽  
Symbol Calculus ◽  
Wave Front Set ◽  
Colombeau Algebras ◽  
Generalized Complex Numbers ◽  
Topological Modules ◽  
Wave Front Sets ◽  
Basic Facts

Summarizing basic facts from abstract topological modules over Colombeau generalized complex numbers we discuss duality of Colombeau algebras. In particular, we focus on generalized delta functional and operator kernels as elements of dual spaces. A large class of examples is provided by pseudodifferential operators acting on Colombeau algebras. By a refinement of symbol calculus we review a new characterization of the wave front set for generalized functions with applications to microlocal analysis. AMS Mathematics Subject Classification (2000): 46F30, 46A20, 47G30.

scholarly journals Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 240
Author(s):  
Sanja Atanasova ◽  
Snježana Maksimović ◽  
Stevan Pilipović
Keyword(s):  
Fourier Transform ◽  
Wave Front ◽  
Short Time Fourier Transform ◽  
Wave Fronts ◽  
Directional Wave ◽  
Tempered Ultradistributions ◽  
Short Time

In this paper we give a characterization of Sobolev k-directional wave front of order p∈[1,∞) of tempered ultradistributions via the directional short-time Fourier transform.

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