Wave propagation on Euclidean surfaces with conical singularities. I: Geometric diffraction

2015/05/05 by G. Austin Ford, Ford, G. Austin, Andrew Hassell +3 · 2 citations
Engineering · Physics and Astronomy · #35L05 #35S30 #58J50 #Analysis of PDEs (math.AP) #Elasticity and Wave Propagation #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1505.01043

openalex publication_date 2015/05/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We investigate the singularities of the trace of the half-wave group, Tr e^-it√Δ, on Euclidean surfaces with conical singularities (X,g). We compute the leading-order singularity associated to periodic orbits with successive degenerate diffractions. This result extends the previous work of the third author \citeHil and the two-dimensional case of the work of the first author and Wunsch \citeForWun as well as the seminal result of Duistermaat and Guillemin \citeDuiGui in the smooth setting. As an intermediate step, we identify the wave propagators on X as singular Fourier integral operators associated to intersecting Lagrangian submanifolds, originally developed by Melrose and Uhlmann \citeMelUhl.

Citations

• The spectral function of an elliptic operator

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