Abels, Helmut and Pfeuffer, Christine (2016) Spectral Invariance of Non-Smooth Pseudo-Differential Operators. INTEGRAL EQUATIONS AND OPERATOR THEORY, 86 (1). pp. 41-70. ISSN 0378-620X, 1420-8989
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We discuss some spectral invariance results for non-smooth pseudodifferential operators with coefficients in Holder spaces in this paper. In analogy to the proof in the smooth case of Beals and Ueberberg, c.f. (Duke Math J 44(1):45-57, 1977; Manuscripta Math 61(4):459-475, 1988), we use the characterization of non-smooth pseudodifferential operators to get such a result. The main new difficulties are the limited mapping properties of pseudodifferential operators with non-smooth symbols and the fact, that in general the composition of two non-smooth pseudodifferential operators is not a pseudodifferential operator. In order to improve these spectral invariance results for certain subsets of non-smooth pseudodifferential operators with coefficients in Holder spaces, we improve the characterization of non-smooth pseudodifferential operators of A. and P., c.f. (Abels and Pfeuffer, Characterization of non-smooth pseudodifferential operators. arXiv:1512.01127,2015).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SOBOLEV SPACES; Non-smooth pseudodifferential operators; characterization by mapping properties; spectral invariance |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 03 Apr 2019 13:20 |
| Last Modified: | 03 Apr 2019 13:20 |
| URI: | https://pred.uni-regensburg.de/id/eprint/3354 |
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