A Periodic Faddeev-Type Solution Operator
A Periodic Faddeev-Type Solution Operator
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DOI：
10.1006/jdeq.1996.0096
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发表时间：
1996-06
影响因子：
2.4
通讯作者：
P. Hähner
中科院分区：
文献类型：
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作者：
P. Hähner
利用Fourier级数构造了有界区域上方程Δu+2i ∈·u= in的周期解算子.证明了当参数|林|都是无限的然后我们应用这些算子证明了满足不等式的函数su ∈C20（Rd| Δu（x）|CIMM| u（x）|在任何地方都必须消失。我们将这一结果推广到其他二阶常系数椭圆型微分算子，以取代拉普拉斯算子。最后，我们利用解算子得到了微分方程解的乘积的跨度在L1中是稠密的。
Abstract We construct periodic solution operators for the equationΔu+2iζ·∇u=fin a bounded domain with the help of Fourier series. We prove that theL2-norms of these operators converge to zero if the parameter |Im ζ| goes to infinity. Then we apply these operators to show that functionsu∈C20(Rd) satisfying an inequality |Δu(x)|⩽M |u(x)| inRdmust vanish everywhere. We extend this result to other second order elliptic differential operators with constant coefficients replacing the Laplacian. Finally, we use the solution operators to derive that the span of products of solutions to differential equations is dense inL1.