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On the relative Nash approximation of analytic maps. (English) Zbl 0911.32012

The authors obtain several results of Nash approximation \(\psi\) of analytic maps (real or complex) \(\varphi:X\to Y\), \(X,Y\) Nash spaces on a Nash subspace \(Z\). s.t. \(\psi|_Z= \varphi|_Z\). These results generalize the authors previous results in the non-singular case, using new results of M. Coste, J. M. Ruiz and M. Shiota [Am. J. Math. 117, No. 4, 905-927 (1995; Zbl 0873.32007)] in case of real spaces, and the result of L. Lempert [Invent. Math. 121, No. 2, 335-353 (1995; Zbl 0837.32008)] for the complex spaces.
Reviewer: Jiye Yu (Madison)

MSC:

32C07 Real-analytic sets, complex Nash functions
58A07 Real-analytic and Nash manifolds
14P20 Nash functions and manifolds
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