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• W2590795732 abstract "We study the functional calculus for operators of the form $$f_h(P(h))$$ within the theory of semiclassical pseudodifferential operators, where $${f_h}_{hin (0,1]}subset mathrm{C^infty _c}({{mathbb {R}}})$$ denotes a family of h-dependent functions satisfying some regularity conditions, and P(h) is either an appropriate self-adjoint semiclassical pseudodifferential operator in $$mathrm{L}^2({{mathbb {R}}}^n)$$ or a Schrödinger operator in $$mathrm{L}^2(M), M$$ being a closed Riemannian manifold of dimension n. The main result is an explicit semiclassical trace formula with remainder estimate that is well-suited for studying the spectrum of P(h) in spectral windows of width of order $$h^delta $$ , where $$0le delta <frac{1}{2}$$ ." @default.
• W2590795732 created "2017-03-03" @default.
• W2590795732 creator A5072590847 @default.
• W2590795732 date "2017-02-22" @default.
• W2590795732 modified "2023-09-26" @default.
• W2590795732 title "On the semiclassical functional calculus for h-dependent functions" @default.
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• W2590795732 doi "https://doi.org/10.1007/s10455-017-9549-1" @default.
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