论文标题
非平滑伪差算子的弗雷德尔姆指数和光谱的不变性
Invariance of the Fredholm Index and Spectrum of Non-Smooth Pseudodifferential Operators
论文作者
论文摘要
在本文中，我们显示了hölder空间中具有系数的非平滑伪差算子的弗雷德霍尔姆指数的不变性。通过这种不变性，我们改善了与Hölder空间系数的非平滑伪差算子$ p $的先前光谱不变性结果。为此，我们将$ p $与平滑的伪差操作员大约近似，并使用光滑的pseudoDifferential oberators的光谱不变性结果。然后，我们获得了光谱不变性的结果，类比是Rabier对非平滑差异操作员的光谱不变性结果的证明。
In this paper we show the invariance of the Fredholm index of non-smooth pseudodifferential operators with coefficients in Hölder spaces. By means of this invariance we improve previous spectral invariance results for non-smooth pseudodifferential operators $P$ with coefficients in Hölder spaces. For this purpose we approximate $P$ with smooth pseudodifferential operators and use a spectral invariance result of smooth pseudodifferential operators. Then we get the spectral invariance result in analogy to a proof of the spectral invariance result for non-smooth differential operators by Rabier.
