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- W4381108663 abstract "The Bochner–Schrödinger operator $$H_{p}=frac 1pDelta^{L^potimes E}+V$$ on tensor powers $$L^p$$ of a Hermitian line bundle $$L$$ twisted by a Hermitian vector bundle $$E$$ on a Riemannian manifold of bounded geometry is studied. For any function $$varphiin mathcal S(mathbb R)$$ , we consider the bounded linear operator $$varphi(H_p)$$ in $$L^2(X,L^potimes E)$$ defined by the spectral theorem and describe an asymptotic expansion of its smooth Schwartz kernel in a fixed neighborhood of the diagonal in the semiclassical limit $$pto infty$$ . In particular, we prove that the trace of the operator $$varphi(H_p)$$ admits a complete asymptotic expansion in powers of $$p^{-1/2}$$ as $$pto infty$$ . We also prove a result on the asymptotic localization of the Schwartz kernel of the spectral projection on the diagonal in the case when the curvature is of full rank." @default.
- W4381108663 created "2023-06-18" @default.
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- W4381108663 date "2023-06-01" @default.
- W4381108663 modified "2023-09-27" @default.
- W4381108663 title "Semiclassical Asymptotic Expansions for Functions of the Bochner–Schrödinger Operator" @default.
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- W4381108663 doi "https://doi.org/10.1134/s1061920823020061" @default.
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