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- W2915980946 abstract "We study the propagator of the wave equation on a closed Riemannian manifold $M$. We propose a geometric approach to the construction of the propagator as a single oscillatory integral global both in space and in time with a distinguished complex-valued phase function. This enables us to provide a global invariant definition of the full symbol of the propagator - a scalar function on the cotangent bundle - and an algorithm for the explicit calculation of its homogeneous components. The central part of the paper is devoted to the detailed analysis of the subprincipal symbol; in particular, we derive its explicit small time asymptotic expansion. We present a general geometric construction that allows one to visualise topological obstructions and describe their circumvention with the use of a complex-valued phase function. We illustrate the general framework with explicit examples in dimension two." @default.
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- W2915980946 date "2022-01-01" @default.
- W2915980946 modified "2023-09-24" @default.
- W2915980946 title "Geometric wave propagator on Riemannian manifolds" @default.
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- W2915980946 doi "https://doi.org/10.4310/cag.2022.v30.n8.a2" @default.
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