Extending analyticK-subanalytic functions

2004 ◽  
Vol 2 (3) ◽  
pp. 362-367
Author(s):  
Artur Piękosz
Keyword(s):  
Subanalytic Functions

Subanalytic Functions

1994 ◽  
Vol 344 (2) ◽  
pp. 583 ◽  
Author(s):  
Adam Parusinski
Keyword(s):  
Subanalytic Functions

scholarly journals Subanalytic functions

1994 ◽  
Vol 344 (2) ◽  
pp. 583-595 ◽  
Author(s):  
Adam Parusiński
Keyword(s):  
Subanalytic Functions

scholarly journals A nonsmooth Morse–Sard theorem for subanalytic functions

2006 ◽  
Vol 321 (2) ◽  
pp. 729-740 ◽  
Author(s):  
Jérôme Bolte ◽  
Aris Daniilidis ◽  
Adrian Lewis
Keyword(s):  
Subanalytic Functions

scholarly journals WAVE FRONT HOLONOMICITY OF -CLASS DISTRIBUTIONS ON NON-ARCHIMEDEAN LOCAL FIELDS

2020 ◽  
Vol 8 ◽  
Author(s):  
AVRAHAM AIZENBUD ◽  
RAF CLUCKERS
Keyword(s):  
Fourier Transform ◽  
Wave Front ◽  
Fourier Transforms ◽  
Stability Result ◽  
Local Fields ◽  
Wave Front Set ◽  
Class A ◽  
Subanalytic Functions ◽  
Wave Front Sets ◽  
The Fourier Transform

Many phenomena in geometry and analysis can be explained via the theory of $D$ -modules, but this theory explains close to nothing in the non-archimedean case, by the absence of integration by parts. Hence there is a need to look for alternatives. A central example of a notion based on the theory of $D$ -modules is the notion of holonomic distributions. We study two recent alternatives of this notion in the context of distributions on non-archimedean local fields, namely $\mathscr{C}^{\text{exp}}$ -class distributions from Cluckers et al. [‘Distributions and wave front sets in the uniform nonarchimedean setting’, Trans. Lond. Math. Soc.5(1) (2018), 97–131] and WF-holonomicity from Aizenbud and Drinfeld [‘The wave front set of the Fourier transform of algebraic measures’, Israel J. Math.207(2) (2015), 527–580 (English)]. We answer a question from Aizenbud and Drinfeld [‘The wave front set of the Fourier transform of algebraic measures’, Israel J. Math.207(2) (2015), 527–580 (English)] by showing that each distribution of the $\mathscr{C}^{\text{exp}}$ -class is WF-holonomic and thus provides a framework of WF-holonomic distributions, which is stable under taking Fourier transforms. This is interesting because the $\mathscr{C}^{\text{exp}}$ -class contains many natural distributions, in particular, the distributions studied by Aizenbud and Drinfeld [‘The wave front set of the Fourier transform of algebraic measures’, Israel J. Math.207(2) (2015), 527–580 (English)]. We show also another stability result of this class, namely, one can regularize distributions without leaving the $\mathscr{C}^{\text{exp}}$ -class. We strengthen a link from Cluckers et al. [‘Distributions and wave front sets in the uniform nonarchimedean setting’, Trans. Lond. Math. Soc.5(1) (2018), 97–131] between zero loci and smooth loci for functions and distributions of the $\mathscr{C}^{\text{exp}}$ -class. A key ingredient is a new resolution result for subanalytic functions (by alterations), based on embedded resolution for analytic functions and model theory.

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