CARLEMAN APPROXIMATION OF MAPS INTO OKA MANIFOLDS

摘要

In this paper we obtain a Carleman approximation theorem for maps from Stein manifolds to Oka manifolds. More precisely, we show that under suitable complex analytic conditions on a totally real set M of a Stein manifold X, every smooth map X -> Y to an Oka manifold Y satisfying the Cauchy-Riemann equations along M up to order k can be C-k-Carleman approximated by holomorphic maps X -> Y. Moreover, if K is a compact O(X)-convex set such that K. M is O(X)-convex, then we can C-k-Carleman approximate maps which satisfy the Cauchy-Riemann equations up to order k along M and are holomorphic on a neighbourhood of K or merely in the interior of K if the latter set is the closure of a strongly pseudoconvex domain.