scholarly journals The theorem of the complement for a quasi subanalytic set

2004 ◽  
Vol 161 (3) ◽  
pp. 225-247
Author(s):  
Abdelhafed Elkhadiri
Keyword(s):  
Subanalytic Set

scholarly journals Global smoothing of a subanalytic set

2018 ◽  
Vol 167 (16) ◽  
pp. 3115-3128 ◽  
Author(s):  
Edward Bierstone ◽  
Adam Parusiński
Keyword(s):  
Subanalytic Set ◽  
Global Smoothing

scholarly journals Uniform Linear Bound in Chevalley’s Lemma

2008 ◽  
Vol 60 (4) ◽  
pp. 721-733
Author(s):  
J. Adamus ◽  
E. Bierstone ◽  
P. D. Milman
Keyword(s):  
Analytic Mapping ◽  
Subanalytic Set

AbstractWe obtain a uniform linear bound for the Chevalley function at a point in the source of an analytic mapping that is regular in the sense of Gabrielov. There is a version of Chevalley’s lemma also along a fibre, or at a point of the image of a proper analytic mapping. We get a uniform linear bound for the Chevalley function of a closed Nash (or formally Nash) subanalytic set.

scholarly journals Invariant Whitney functions

2019 ◽  
Vol 30 (02) ◽  
pp. 1950009
Author(s):  
Hans-Christian Herbig ◽  
Markus J. Pflaum
Keyword(s):  
Lie Group ◽  
Invariant Function ◽  
Compact Lie Group ◽  
Similar Statement ◽  
Real Vector ◽  
Linear Action ◽  
Smooth Functions ◽  
Finite Dimensional ◽  
Subanalytic Set ◽  
Whitney Functions

Theorem 1 of [G. W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975) 63–68.] says that for a linear action of a compact Lie group [Formula: see text] on a finite dimensional real vector space [Formula: see text], any smooth [Formula: see text]-invariant function on [Formula: see text] can be written as a composite with the Hilbert map. We prove a similar statement for the case of Whitney functions along a subanalytic set [Formula: see text] fulfilling some regularity assumptions. In order to deal with the case when [Formula: see text] is not [Formula: see text]-stable, we use the language of groupoids.

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