论文标题
矢量值功能和扩展运算符的平滑操作员
Smoothing operators for vector-valued functions and extension operators
论文作者
论文摘要
For suitable finite-dimensional smooth manifolds M (possibly with various kinds of boundary or corners), locally convex topological vector spaces F and non-negative integers k, we construct continuous linear operators S_n from the space of F-valued k times continuously differentiable functions on M to the corresponding space of smooth functions such that S_n(f) converges to f in C^k(M,F) as n tends to无穷大，在c^k（m，f）的紧凑子集中均均匀。如果L是M的闭合子集，则我们还研究了从C^K（M，F）到C^K（L，F）的限制图的连续线性右对的存在，并具有C^k-manifold结构，将包含图从L到M转变为C^K-MAP。此外，我们在许多情况下在矢量束的截面空间之间构建连续的线性右对，以构建限制运算符，并平滑局部权利倒置，以在映射的流形之间限制运算符。我们还获得了纤维束中部分的平滑结果。
For suitable finite-dimensional smooth manifolds M (possibly with various kinds of boundary or corners), locally convex topological vector spaces F and non-negative integers k, we construct continuous linear operators S_n from the space of F-valued k times continuously differentiable functions on M to the corresponding space of smooth functions such that S_n(f) converges to f in C^k(M,F) as n tends to infinity, uniformly for f in compact subsets of C^k(M,F). We also study the existence of continuous linear right inverses for restriction maps from C^k(M,F) to C^k(L,F) if L is a closed subset of M, endowed with a C^k-manifold structure turning the inclusion map from L to M into a C^k-map. Moreover, we construct continuous linear right inverses for restriction operators between spaces of sections in vector bundles in many situations, and smooth local right inverses for restriction operators between manifolds of mappings. We also obtain smoothing results for sections in fibre bundles.
