Holomorphic approximation on real submanifolds of a complex manifold

Compact groups operating on Banach algebras

“…that rank(F,,) =0, then an easy and wetlknown result (see [9]) gives H = C(dp(G)) and hence A = C(G) by the previous identifications.…”

Uniform approximation on manifolds

“…The case when M is of class C ∞ and E is empty is in papers by Nirenberg and Wells [17], [18]. The case when M is an m-dimensional manifold of class C r with r ≥ (m/2) + 1 (and E is arbitrary) is in a paper of Hörmander and Wermer [12].…”

Approximation theorems on differentiable submanifolds of a complex manifold

“…Some of the results of this paper were announced in [12]. For real-analytic submanifolds, an independent proof of our principal result (Theorem 6.1) (in its original form) was given in [15], and has been extended to certain classes of realanalytic subvarieties [18].…”

“…from a totally real submanifold M of a smooth function m on M so that du vanishes to high order on M (the formal Cauchy-Kovalevsky theorem in this situation) and then solving a d-Neumann problem in an appropriate tubular neighborhood was outlined in a letter to the second author in 1965. The original proofs of some of the theorems presented here (as outlined in [12]) were based on this technique along with a detailed analysis of the dependence on the domain of the estimates in [10]. At a later date Hörmander pointed out the applicability of Proposition 5.4 to this problem, enabling us to simplify our analysis considerably, by allowing us to use the L2 estimates of [7].…”