Calderon投影的新定义及其应用
The Calderon Projection: New Definition and Applications
摘要：
本文考虑具有光滑边界N的紧致光滑流形M上作用于复向量丛E，F的截面之间的任意线性椭圆型一阶微分算子A.我们描述了A在N的领邻域U中的解析性质和拓扑性质，并分析了A的各种写法|产品形式的U。讨论了相应切算子的扇形投影，通过适当的局部边界条件构造了A的各种可逆双算子，得到了具有不同映射性质的Poisson型算子，并给出了Calderon投影的一个典型构造.我们应用我们的构造推广了协证定理，并确定了Calderon投影连续变分的充分条件和数据连续变分下适定的自伴Fredholm扩张的充分条件.
英文摘要：
We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting between sections of complex vector bundles E,F over a compact smooth manifold M with smooth boundary N. We describe the analytic and topological properties of A in a collar neighborhood U of N and analyze various ways of writing A|U in product form. We discuss the sectorial projections of the corresponding tangential operator, construct various invertible doubles of A by suitable local boundary conditions, obtain Poisson type operators with different mapping properties, and provide a canonical construction of the Calderon projection. We apply our construction to generalize the Cobordism Theorem and to determine sufficient conditions for continuous variation of the Calderon projection and of well--posed selfadjoint Fredholm extensions under continuous variation of the data.
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