Functional calculus for Safarov pseudo-differential operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914080531415040 |
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| author | Cobos, Santiago Gómez Ruzhansky, Michael |
| author_facet | Cobos, Santiago Gómez Ruzhansky, Michael |
| contents | Given a smooth, closed Riemannian manifold $(M,g)$ equipped with a linear connection $\nabla$ (not necessarily metric), we develop the holomorphic functional calculus for operators belonging to the global pseudo-differential classes $Ψ_{ρ, δ}^m\left(Ω^κ, \nabla, τ\right)$ introduced by Safarov. As a consequence of our main result, we establish a Szegö type-theorem, derive asymptotic expansion of the heat kernel trace, and calculate some associated spectral $ζ$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional calculus for Safarov pseudo-differential operators Cobos, Santiago Gómez Ruzhansky, Michael Analysis of PDEs Functional Analysis 58J40 (Primary) 35S05, 47A60 (Secondary) Given a smooth, closed Riemannian manifold $(M,g)$ equipped with a linear connection $\nabla$ (not necessarily metric), we develop the holomorphic functional calculus for operators belonging to the global pseudo-differential classes $Ψ_{ρ, δ}^m\left(Ω^κ, \nabla, τ\right)$ introduced by Safarov. As a consequence of our main result, we establish a Szegö type-theorem, derive asymptotic expansion of the heat kernel trace, and calculate some associated spectral $ζ$-functions. |
| title | Functional calculus for Safarov pseudo-differential operators |
| topic | Analysis of PDEs Functional Analysis 58J40 (Primary) 35S05, 47A60 (Secondary) |
| url | https://arxiv.org/abs/2510.06859 |