A Volterra Calculus for Lie Groupoids
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917055196823552 |
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| author | Bohlen, Karsten |
| author_facet | Bohlen, Karsten |
| contents | A pseudodifferential Volterra calculus for inverting parabolic differential equations on Lie groupoids is introduced. This enables the study of fundamental solutions of various cases of heat flows on singular manifolds with corners with non-resonant boundary indicial symbols, such as the $b$-manifolds, as well as other geometric bisection covariant heat flows. We also establish the short time asymptotic expansion for the heat kernel of a positive, elliptic differential operator on a Lie groupoid that acts on suitable Sobolev Hilbert modules and is positive definite with respect to the appropriate $L^2$ inner product. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_00991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Volterra Calculus for Lie Groupoids Bohlen, Karsten Analysis of PDEs 47J35, 58H05, 35K67 A pseudodifferential Volterra calculus for inverting parabolic differential equations on Lie groupoids is introduced. This enables the study of fundamental solutions of various cases of heat flows on singular manifolds with corners with non-resonant boundary indicial symbols, such as the $b$-manifolds, as well as other geometric bisection covariant heat flows. We also establish the short time asymptotic expansion for the heat kernel of a positive, elliptic differential operator on a Lie groupoid that acts on suitable Sobolev Hilbert modules and is positive definite with respect to the appropriate $L^2$ inner product. |
| title | A Volterra Calculus for Lie Groupoids |
| topic | Analysis of PDEs 47J35, 58H05, 35K67 |
| url | https://arxiv.org/abs/2511.00991 |