Fredholm Criteria for $G$-pseudodifferential Operators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909043641024512 |
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| author | Baldare, Alexandre Savin, Anton Yu. Schrohe, Elmar |
| author_facet | Baldare, Alexandre Savin, Anton Yu. Schrohe, Elmar |
| contents | Let $G$ be a compact Lie group that acts smoothly on a closed manifold $M$. Using a general Simonenko principle, we derive a novel criterion for the Fredholm property of $G$-pseudodifferential operators acting on Sobolev spaces of sections of vector bundles over $M$. In case the group is finite, we obtain a further characterization of the Fredholm property of $G$-pseudodifferential operators in terms of the invertibility of suitable symbols. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_14778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fredholm Criteria for $G$-pseudodifferential Operators Baldare, Alexandre Savin, Anton Yu. Schrohe, Elmar Differential Geometry Analysis of PDEs Functional Analysis Operator Algebras 47A53, 58J40, 47L80, 46N20 Let $G$ be a compact Lie group that acts smoothly on a closed manifold $M$. Using a general Simonenko principle, we derive a novel criterion for the Fredholm property of $G$-pseudodifferential operators acting on Sobolev spaces of sections of vector bundles over $M$. In case the group is finite, we obtain a further characterization of the Fredholm property of $G$-pseudodifferential operators in terms of the invertibility of suitable symbols. |
| title | Fredholm Criteria for $G$-pseudodifferential Operators |
| topic | Differential Geometry Analysis of PDEs Functional Analysis Operator Algebras 47A53, 58J40, 47L80, 46N20 |
| url | https://arxiv.org/abs/2605.14778 |