On the relative Nash approximation of analytic maps (Q1128212)

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 \textit{M. Coste}, \textit{J. M. Ruiz} and \textit{M. Shiota} [Am. J. Math. 117, No. 4, 905-927 (1995; Zbl 0873.32007)] in case of real spaces, and the result of \textit{L. Lempert} [Invent. Math. 121, No. 2, 335-353 (1995; Zbl 0837.32008)] for the complex spaces.