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arXiv · 1802.00143

Invariant Whitney Functions

Hans-Christian Herbig·Markus J. Pflaum
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Abstract

A theorem of Gerald Schwarz [24, Thm. 1] says that for a linear action of a compact Lie group $G$ on a finite dimensional real vector space $V$ any smooth $G$-invariant function on $V$ 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 $Z\subset V$ fulfilling some regularity assumptions. In order to deal with the case when $Z$ is not $G$-stable we use the language of groupoids.

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Hans-Christian Herbig, Markus J. Pflaum. 2018-02-01. Invariant Whitney Functions. https://doi.org/10.1142/s0129167x19500095

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