"Invariance of the Fredholm Index of Non-Smooth Pseudodifferential Operators"Pfeuffer, ChristineAs nearly invertible operators Fredholm operators play an important role in the field of partial differential equations in order to obtain existence and uniqueness results. Hence great effort already was spent to get some conditions for the Fredholmness of pseudodifferential operators. However, there are very few results for the invariance of the Fredholm index of such operators. In the smooth case Schrohe was able to show under certain conditions, that the Fredholm index of smooth pseudodifferential operators is invariant considered as a map between certain weighted Bessel potential spaces with symbols in the H\"ormander-class $S^m_{1,0}(\mathbb{R}^n\times \mathbb{R}^n)$. In applications also non-smooth pseudodifferential operators occur. The goal of this talk is to show the invariance of the Fredholm index for non-smooth pseudodifferential operators with symbols in the class $C^{\tilde{m},s}S^m_{1,0}(\mathbb{R}^n \times \mathbb{R}^n)$. To reach this aim we use the main idea of the result from Rabier about the Fredholm index for non-smooth differential operators. The main difficulty is to prove a regularity result for non-smooth pseudodifferential operators needed in the proof. The talk is based on a joint work with H.\ Abels. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Pfeuffer_2022-02_abstract_Pfeuffer_Christine.pdf |
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